title: Infant baptism

text: Presbyterian, Congregational and Reformed Christians believe that baptism, whether of infants or adults, is a "sign and seal of the covenant of grace", and that baptism admits the party baptized into the visible church. Being a member of the visible church does not guarantee salvation; though it does provide the child with many benefits, including that of one's particular congregation consenting to assist in the raising of that child in "the way he should go, (so that) when he is old he will not turn from it". Elect infants (those predestined for salvation) who die in infancy are by faith considered regenerate on the basis of God's covenant promises in the covenant of grace.


title: Infant baptism

text: Presbyterian, Congregational and many Reformed Christians see infant baptism as the New Testament form of circumcision in the Jewish covenant. Circumcision did not create faith in the 8-day-old Jewish boy. It merely marked him as a member of God's covenant people Israel. Likewise, baptism doesn't create faith; it is a sign of membership in the visible covenant community.


title: Infant baptism

text: Presbyterian, Congregational and Reformed Christians consider children of professing Christians to be members of the visible Church (the covenant community). They also consider them to be full members of the local congregation where their parents are members and members of the universal Church (the set of all true believers who make up the invisible church) unless and until they prove otherwise. Baptism is the mark of membership in the covenant of grace and in the universal church, although regeneration is not inseparably connected with baptism.


title: Infant baptism

text: Infant baptism can be contrasted with what is called "believer's baptism" (or credobaptism, from the Latin word "credo" meaning "I believe"), which is the religious practice of baptising only individuals who personally confess faith in Jesus, therefore excluding underage children.


title: Infant baptism

text: Pedobaptism and credobaptism are positions which bubble up from theological views at a more fundamental level of one's theological system.


title: Infant baptism

text: Christians who practice infant baptism do not completely agree on the reasons for doing so, and offer different reasons in support of the practice. Among the arguments made in support of the practice are:


title: Infant baptism

text: Trinitarian Christian denominations that oppose infant baptism include the International Christian Church, all Baptist and Anabaptist traditions and denominations, Pentecostals, Assemblies of God and more.


title: Infant baptism

text: Several nontrinitarian religious groups also oppose infant baptism, including Oneness Pentecostals, Christadelphians, Jehovah's Witnesses, United Church of God, and the Church of Jesus Christ of Latter-day Saints.


title: Infant baptism

text: B.R. White describes the motivations behind persecution of the Anabaptists during the Reformation as follows:


title: Infant baptism

text: Other Christians saw the baptism of each new-born baby into the secular parish community and close links between church and state as the divinely-ordained means of holding society together. Hence many other Christians saw the Anabaptists as subversive of all order. Consequently, from the earliest days, they were sharply persecuted and leaders were soon executed.


title: Infant baptism

text: The Church of Jesus Christ of Latter-day Saints (LDS Church) completely rejects infant baptism. Little children are considered both born without sin and incapable of committing sin. They have no need of baptism until age eight, when they can begin to learn to discern right from wrong, and are thus accountable to God for their own actions. However, the LDS Church performs a non-saving ordinance to name and bless children, customarily performed on infants.


title: Infant baptism

text: For Roman Catholic and Methodist Christians, Confirmation "strengthens" (the original meaning of the word "confirm") the grace of Baptism, by conferring an increase and deepening of that grace.


title: Infant baptism

text: In Eastern Christianity, including the Eastern Catholic Churches, the sacrament of Confirmation is conferred immediately after baptism, and there is no renewal of baptismal promises. In the Latin-Rite (i.e. Western) Catholic Church, the sacrament is to be conferred at about the age of discretion (generally taken to be about 7), unless the Episcopal Conference has decided on a different age, or there is danger of death or, in the judgement of the minister, a grave reason suggests otherwise (canon 891 of the Code of Canon Law). The renewal of baptismal promises by those receiving the sacrament in the Western Catholic Church is incidental to the rite and not essentially different from the solemn renewal of their baptismal promises that is asked of all members of this Church each year at the Easter Vigil service. Only in French-speaking countries has there been a development of ceremonies, quite distinct from the sacrament of Confirmation, for young Catholics to profess their faith publicly, in line with their age.


title: Infant baptism

text: Within the Church of Jesus Christ of Latter-day Saints, confirmation or "the laying on of hands" is an essential part of the baptismal ordinance, and to receive baptism without confirmation is to leave the ordinance incomplete. Confirmation is the conferring of the gift of the Holy Ghost as a constant companion. To confirm means to "make more sure" and the ordinance of confirmation stands as a witness of the individual becoming a member of the LDS Church and not just an acceptance of Jesus.


title: Infant baptism

text: According to legal professor and former Irish president Mary McAleese, as outlined in her doctoral thesis, infant baptism amounts to "enforced membership of the Catholic Church", which violates fundamental rights of children. These "infant conscripts ... are held to lifelong obligations of obedience" without their understanding or consent. "Parents can guide and direct [their children] but they can't impose, and what the church has failed to do is to recognise that there has to be a point at which our young people, as adults who have been baptised into the church and raised in the faith, have the chance to say 'I validate this' or 'I repudiate this'. You and I know, we live now in times where we have the right to freedom of conscience, freedom of belief, freedom of opinion, freedom of religion and freedom to change religion. The Catholic Church yet has to fully embrace that thinking."


title: Infant baptism

text: Baptisms have sometimes accidentally led to injuries, or deaths, such as drowning deaths, to babies. In Romania, this has served as an opportunity to revise practices.


title: Infant baptism

text: In Yazidism, children are baptised at birth and circumcision is not required, but is practised by some due to regional customs. The Yazidi baptism is called "Mor kirin" (literally: 'to seal'). Traditionally, Yazidi children are baptised at birth with water from the "Kaniya Sipî" ('White Spring') at Lalish. It involves pouring holy water from the spring on the child's head three times.


title: Southern Conference

text: The Southern Conference (SoCon) is a collegiate athletic conference affiliated with the National Collegiate Athletic Association (NCAA) Division I. Southern Conference football teams compete in the Football Championship Subdivision (formerly known as Division I-AA). Member institutions are located in the states of Alabama, Georgia, North Carolina, South Carolina, Tennessee, and Virginia.


title: Southern Conference

text: Established in 1921, the Southern Conference ranks as the fifth-oldest major college athletic conference in the United States, and either the third- or fourth-oldest in continuous operation, depending on definitions. Among conferences currently in operation, the Big Ten (1896) and Missouri Valley (1907) are indisputably older. The Pac-12 Conference did not operate under its current charter until 1959, but claims the history of the Pacific Coast Conference, founded in 1915, as its own. The Southwest Conference (SWC) was founded in 1914, but ceased operation in 1996. The Big Eight Conference claimed the same history as the Missouri Valley from 1907 to 1928 during its existence; though it essentially merged with four SWC members to form the Big 12 Conference in 1996, the Big 12 does not claim the Big Eight's legacy. The Ivy League was formally organized in 1954 with athletic competition starting in 1955, but claims the history of the Eastern Intercollegiate Basketball League, which competed from 1901 to 1955, as its own.


title: Southern Conference

text: The SoCon was the first conference to use the three-point field goal in basketball in a November 29, 1980 game at Western Carolina against Middle Tennessee State University (MTSU), where Ronnie Carr shot the historic shot from away and the Catamounts won 77–70.


title: Southern Conference

text: The Southern Conference is considered one of the stronger football conferences in the Football Championship Subdivision and is considered a mid-major conference in basketball. The three-time Division I NCAA Football champion Appalachian State Mountaineers were a member of the conference when they stunned the fifth-ranked Michigan Wolverines 34–32 on September 1, 2007. The Davidson Wildcats reached the Elite Eight in the 2008 NCAA Men's Division I Basketball Tournament by upsetting power programs Gonzaga, Georgetown, and Wisconsin. More recently, the six-time Division I NCAA Football champion Georgia Southern Eagles stunned Southeastern Conference power-house Florida Gators 26–20 in The Swamp on November 23, 2013—the first loss to a lower division opponent in the Florida program's history. In 2015, Furman defeated UCF 16–15 and The Citadel topped South Carolina 23–22 for their second win over the Gamecocks in the past three meetings. On September 4, 2021, East Tennessee State University stunned Vanderbilt 23–3 at their opening game. The SoCon also frequently sees multiple teams selected to participate in the NCAA Division I Baseball Championship.


title: Southern Conference

text: Talks of a new conference for Southern athletics had started as early as fall of 1920. The conference was formed on February 25, 1921 in Atlanta as fourteen member institutions split from the Southern Intercollegiate Athletic Association. Southern Conference charter members were Alabama, Auburn, Clemson, Georgia, Georgia Tech, Kentucky, Maryland, Mississippi State, North Carolina, North Carolina State, Tennessee, Virginia, Virginia Tech, and Washington & Lee. In 1922, six more universities – Florida, LSU, Mississippi, South Carolina, Tulane, and Vanderbilt joined the conference. The first year of competition for the conference was in 1922, effective January 1. The new rules banned freshman play. Later additions included (1924), Virginia Military Institute (1924), and Duke (1929).


title: Southern Conference

text: The SoCon is particularly notable for having spawned two other major conferences. In 1932, the 13 schools located south and west of the Appalachians (Alabama, Auburn, Florida, Georgia, Georgia Tech, Kentucky, LSU, Mississippi, Mississippi State, University of the South (Sewanee), Tennessee, Tulane, and Vanderbilt) all departed the SoCon to form the Southeastern Conference (SEC). In 1953, seven additional schools (Clemson, Duke, Maryland, North Carolina, North Carolina State, South Carolina, and Wake Forest) withdrew from the SoCon to form the Atlantic Coast Conference (ACC). The SEC and ACC have gone on to surpass their parent conference in prestige; while the SEC and ACC are considered "power" conferences in Division I FBS (formerly Division I-A), the SoCon dropped to Division I-AA (FCS) in 1982, four years after the top division was split into two levels in 1978.


title: Southern Conference

text: The SoCon became the first league to hold a post-season basketball tournament to decide a conference champion. Although first played in 1921, it did not become "official" until 1922, and in its first few years included teams which were not conference members. Held at the Municipal Auditorium in Atlanta from February 24 – March 2, 1922, the first meeting was won by North Carolina who defeated non-member Mercer in the Finals 40–25. The SoCon Basketball Tournament continues as the nation's oldest conference tournament. The next-oldest tournament overall is the SEC men's basketball tournament, founded in 1933, but that event was suspended after its 1952 edition and did not resume until 1979. With the demise of the Division II West Virginia Intercollegiate Athletic Conference in 2013, whose tournament had been continuously held since 1936, the next-oldest conference tournament in continuous existence is now the ACC men's basketball tournament, first held in 1954.


title: Southern Conference

text: The all-sports membership changed to 10 schools in 2014 following the departure of Appalachian State, Davidson, Elon, and Georgia Southern, plus the arrival of East Tennessee State (ETSU), Mercer, and VMI. The current football membership stands at nine. UNC Greensboro does not sponsor football, while ETSU relaunched its previously dormant football program in 2015 and rejoined SoCon football in 2016 after one season as an independent.


title: Southern Conference

text: On January 9, 2014, the SoCon and Atlantic Sun Conference, now known as the ASUN Conference, announced a new alliance in lacrosse that took effect with the 2015 spring season (2014–15 school year). Under its terms, sponsorship of men's lacrosse shifted from the ASUN to the SoCon, while women's lacrosse sponsorship remained with the ASUN. Bellarmine, which had announced it would join the ASUN for men's lacrosse for the 2015 spring season, instead joined the SoCon. The alliance remains in effect in men's lacrosse, but the leagues amicably ended their full alliance in women's lacrosse once the SoCon began sponsoring that sport in the 2018 spring season (2017–18 school year). However, the conferences maintained their working relationship in women's lacrosse, with the SoCon adding Coastal Carolina as an associate member effective with the 2021 spring season (2020–21 school year) in order to keep both conferences at five women's lacrosse members for 2021. Coastal was intended to play in SoCon women's lacrosse in the 2022 spring season (2021–22 school year) as well, but the SoCon decided to drop the sport after the 2021 spring season (2020–21 school year). While no formal announcement was made, the SoCon–ASUN women's lacrosse partnership definitively ended at that time, as the three full SoCon members who sponsored women's lacrosse moved that sport to the Big South Conference. Coastal and Delaware State both returned women's lacrosse to the ASUN Conference.


title: Southern Conference

text: The men's lacrosse partnership took a slightly different form from the 2022 spring season (2021–22 school year) forward, as the ASUN reinstated its men's lacrosse league. The two full ASUN members with men's lacrosse programs separated, with Jacksonville remaining in SoCon men's lacrosse while Bellarmine joined the ASUN men's lacrosse league. SoCon associate Air Force also left for ASUN men's lacrosse. The SoCon maintained its automatic NCAA tournament berth with the addition of Hampton.


title: Southern Conference

text: Before the addition of Hampton men's lacrosse, the most recent addition to the associate membership was Presbyterian wrestling, which joined during summer 2019. Two women's lacrosse members, Central Michigan and Detroit Mercy, left after the 2020 season (2019–20 school year) to join the new women's lacrosse league of Central's full-time home of the Mid-American Conference; this move contributed to the eventual demise of the SoCon women's lacrosse league.


title: Southern Conference

text: Men's soccer member Belmont will leave the SoCon after the 2021–22 school year when it joins the Missouri Valley Conference, which sponsors that sport. At the same time, Hampton will move men's lacrosse to its new full-time home of the Colonial Athletic Association.


title: Southern Conference

text: The addition of men's lacrosse by the Atlantic 10 Conference, announced on May 23, 2022, led to the demise of the SoCon men's lacrosse league after the 2022 season. In addition to Hampton joining the CAA, SoCon associate members High Point and Richmond (the latter a full A-10 member) moved to the A-10, and Jacksonville returned to ASUN men's lacrosse.


title: Southern Conference

text: In the table below, the "Joined" column denotes the start of the school year in which the institution became an associate member, which for spring sports differs from the first season of competition.


title: Southern Conference

text: Most former members are currently members of either the Southeastern Conference or the Atlantic Coast Conference. Two of the former full members, Appalachian State and Davidson, maintain SoCon associate membership in wrestling. A third former full member, Georgia Southern, became an associate member in rifle when the SoCon added the sport for the 2016–17 school year.


title: Southern Conference

text: In the table below, the "Joined" and "Left" columns denotes the calendar year in which each school joined and left the SoCon. For fall sports, the year of departure differs from the final year of competition. For spring sports, the year of arrival differs from the first season of competition.


title: Southern Conference

text: The Southern Conference sponsors championship competition in 11 men's, 9 women's, and one coeducational NCAA-sanctioned sports. Five schools are associate members for wrestling. Under a cooperative agreement with the ASUN Conference, the SoCon began sponsoring men's lacrosse in the 2014–15 school year (2015 season) with three full members (Furman, Mercer, VMI) and four associates (Bellarmine, High Point, Jacksonville, Richmond). SoCon men's lacrosse has since added Air Force. Women's lacrosse was sponsored by the ASUN through the 2017 season, after which the SoCon launched its own women's lacrosse league. Beginning in the 2016–17 academic year, after a 30-year hiatus, the SoCon resumed rifle as its 21st sport. Members for conference competition are full members The Citadel, VMI, and Wofford as well as associate members UAB, Georgia Southern, and North Georgia. The SoCon is one of only two all-sports conferences to sponsor rifle, joining the Ohio Valley Conference. Rifle is technically a men's sport for NCAA purposes, but men's, women's, and coed teams all compete against each other. Women's lacrosse was added as the 22nd sport for 2017–18, but was dropped after the 2020–21 school year.


title: Southern Conference

text: The SoCon dropped men's lacrosse after the 2022 season. Affiliate member Hampton joined the Colonial Athletic Association, which sponsors that sport, and the Atlantic 10 Conference, full-time home to men's lacrosse affiliate Richmond, launched a men's lacrosse league in the 2023 season, also taking in another SoCon affiliate in High Point. With SoCon men's lacrosse being gutted by these changes, VMI moved that sport to its former men's lacrosse home of the Metro Atlantic Athletic Conference, and the two remaining men's lacrosse members, Jacksonville and Mercer, moved that sport to the ASUN.


title: Southern Conference

text: "This is a partial list of the last 10 champions. For the full history, see List of Southern Conference football champions."


title: Southern Conference

text: "This is a partial list of the last 10 regular-season and tournament champions. For the full history, see List of Southern Conference men's basketball champions."


title: Southern Conference

text: The Southern Conference split into a divisional format for basketball beginning with the 1994–95 season.


title: Southern Conference

text: "This is a partial list of the last 10 tournament champions. For the full history, see Southern Conference women's basketball tournament"


title: Southern Conference

text: "This is a partial list of the last 10 champions. For the full history, see Southern Conference baseball tournament."


title: Southern Conference

text: The Commissioner's and Germann Cups are awarded each year to the top men's and women's program in the conference. The Commissioner's Cup was inaugurated in 1970. The Germann Cup, named for former Southern Conference Commissioner Ken Germann, was first awarded in 1987. The completion of the 2013–2014 athletics season saw Appalachian State winning its 33rd Commissioner's Cup and Furman its 13th Germann Cup.


title: Jordan normal form

text: is an upper triangular matrix of a particular form called a Jordan matrix representing a linear operator on a finite-dimensional vector space with respect to some basis. Such a matrix has each non-zero off-diagonal entry equal to 1, immediately above the main diagonal (on the superdiagonal), and with identical diagonal entries to the left and below them.


title: Jordan normal form

text: Let "V" be a vector space over a field "K". Then a basis with respect to which the matrix has the required form exists if and only if all eigenvalues of the matrix lie in "K", or equivalently if the characteristic polynomial of the operator splits into linear factors over "K". This condition is always satisfied if "K" is algebraically closed (for instance, if it is the field of complex numbers). The diagonal entries of the normal form are the eigenvalues (of the operator), and the number of times each eigenvalue occurs is called the algebraic multiplicity of the eigenvalue.


title: Jordan normal form

text: If the operator is originally given by a square matrix "M", then its Jordan normal form is also called the Jordan normal form of "M". Any square matrix has a Jordan normal form if the field of coefficients is extended to one containing all the eigenvalues of the matrix. In spite of its name, the normal form for a given "M" is not entirely unique, as it is a block diagonal matrix formed of Jordan blocks, the order of which is not fixed; it is conventional to group blocks for the same eigenvalue together, but no ordering is imposed among the eigenvalues, nor among the blocks for a given eigenvalue, although the latter could for instance be ordered by weakly decreasing size.


title: Jordan normal form

text: The Jordan–Chevalley decomposition is particularly simple with respect to a basis for which the operator takes its Jordan normal form. The diagonal form for diagonalizable matrices, for instance normal matrices, is a special case of the Jordan normal form.


title: Jordan normal form

text: The Jordan normal form is named after Camille Jordan, who first stated the Jordan decomposition theorem in 1870.


title: Jordan normal form

text: Some textbooks have the ones on the subdiagonal; that is, immediately below the main diagonal instead of on the superdiagonal. The eigenvalues are still on the main diagonal.


title: Jordan normal form

text: An "n" × "n" matrix "A" is diagonalizable if and only if the sum of the dimensions of the eigenspaces is "n". Or, equivalently, if and only if "A" has "n" linearly independent eigenvectors. Not all matrices are diagonalizable; matrices that are not diagonalizable are called defective matrices. Consider the following matrix:


title: Jordan normal form

text: Including multiplicity, the eigenvalues of "A" are "λ" = 1, 2, 4, 4. The dimension of the eigenspace corresponding to the eigenvalue 4 is 1 (and not 2), so "A" is not diagonalizable. However, there is an invertible matrix "P" such that "J" = "P""AP", where


title: Jordan normal form

text: The matrix formula_3 is almost diagonal. This is the Jordan normal form of "A". The section "Example" below fills in the details of the computation.


title: Jordan normal form

text: So there exists an invertible matrix "P" such that "P""AP" = "J" is such that the only non-zero entries of "J" are on the diagonal and the superdiagonal. "J" is called the Jordan normal form of "A". Each "J" is called a Jordan block of "A". In a given Jordan block, every entry on the superdiagonal is 1.


title: Jordan normal form

text: Consider the matrix formula_7 from the example in the previous section. The Jordan normal form is obtained by some similarity transformation:


title: Jordan normal form

text: For formula_18 we have formula_19, that is, formula_11 is an eigenvector of formula_7 corresponding to the eigenvalue formula_22. For formula_23, multiplying both sides by formula_24 gives


title: Jordan normal form

text: This shows that the eigenvalues are 1, 2, 4 and 4, according to algebraic multiplicity. The eigenspace corresponding to the eigenvalue 1 can be found by solving the equation "Av" = "λv". It is spanned by the column vector "v" = (−1, 1, 0, 0). Similarly, the eigenspace corresponding to the eigenvalue 2 is spanned by "w" = (1, −1, 0, 1). Finally, the eigenspace corresponding to the eigenvalue 4 is also one-dimensional (even though this is a double eigenvalue) and is spanned by "x" = (1, 0, −1, 1). So, the geometric multiplicity (that is, the dimension of the eigenspace of the given eigenvalue) of each of the three eigenvalues is one. Therefore, the two eigenvalues equal to 4 correspond to a single Jordan block, and the Jordan normal form of the matrix "A" is the direct sum


title: Jordan normal form

text: There are three Jordan chains. Two have length one: {"v"} and {"w"}, corresponding to the eigenvalues 1 and 2, respectively. There is one chain of length two corresponding to the eigenvalue 4. To find this chain, calculate


title: Jordan normal form

text: where "I" is the 4 × 4 identity matrix. Pick a vector in the above span that is not in the kernel of "A" − 4"I"; for example, "y" = (1,0,0,0). Now, ("A" − 4"I")"y" = "x" and ("A" − 4"I")"x" = 0, so {"y", "x"} is a chain of length two corresponding to the eigenvalue 4.


title: Jordan normal form

text: The transition matrix "P" such that "P""AP" = "J" is formed by putting these vectors next to each other as follows


title: Jordan normal form

text: If we had interchanged the order in which the chain vectors appeared, that is, changing the order of "v", "w" and {"x", "y"} together, the Jordan blocks would be interchanged. However, the Jordan forms are equivalent Jordan forms.


title: Jordan normal form

text: Given an eigenvalue "λ", every corresponding Jordan block gives rise to a Jordan chain of linearly independent vectors "p, i = "1", ..., b", where "b" is the size of the Jordan block. The generator, or lead vector, "p" of the chain is a generalized eigenvector such that ("A" − "λI)"p" = 0. The vector "p" = ("A" − "λI)"p" is an ordinary eigenvector corresponding to "λ". In general, "p" is a preimage of "p" under "A" − "λI. So the lead vector generates the chain via multiplication by "A" − "λI. Therefore the statement that every square matrix "A" can be put in Jordan normal form is equivalent to the claim that the underlying vector space has a basis composed of Jordan chains.


title: Jordan normal form

text: We give a proof by induction that any complex-valued square matrix "A" may be put in Jordan normal form. Since the underlying vector space can be shown to be the direct sum of invariant subspaces associated with the eigenvalues, "A" can be assumed to have just one eigenvalue "λ". The 1 × 1 case is trivial. Let "A" be an "n" × "n" matrix. The range of "A" − "λI, denoted by Ran("A" − "λI), is an invariant subspace of "A". Also, since "λ" is an eigenvalue of "A", the dimension of Ran("A" − "λI), "r", is strictly less than "n", so, by the inductive hypothesis, Ran("A" − "λI) has a basis {"p", …, "p"} composed of Jordan chains.


title: Jordan normal form

text: the desired result follows immediately from the rank–nullity theorem. (This would be the case, for example, if "A" were Hermitian.)


title: Jordan normal form

text: let the dimension of "Q" be "s" ≤ "r". Each vector in "Q" is an eigenvector, so Ran("A" − "λ"I) must contain "s" Jordan chains corresponding to "s" linearly independent eigenvectors. Therefore the basis {"p", ..., "p"} must contain "s" vectors, say {"p", ..., "p"}, that are lead vectors of these Jordan chains. We can "extend the chains" by taking the preimages of these lead vectors. (This is the key step.) Let "q" be such that


title: Jordan normal form

text: The set {"q"}, being preimages of the linearly independent set {"p"} under "A" − λ I, is also linearly independent. Clearly no non-trivial linear combination of the "q" can lie in ker("A" − "λI"), for {"p"} is linearly independent. Furthermore, no non-trivial linear combination of the "q" can belong to Ran("A" − "λ" I) because it would then be a linear combination of the basic vectors "p", ..., "p", and this linear combination would have a contribution of basic vectors not in ker("A" − "λI") because otherwise it would belong to ker("A" − "λI"). The action of "A" − "λI" on both linear combinations would then produce an equality of a non-trivial linear combination of lead vectors and such a linear combination of non-lead vectors, which would contradict the linear independence of ("p", ..., "p").


title: Jordan normal form

text: Each "z" forms a Jordan chain of length 1. By construction, the union of the three sets {"p", ..., "p"}, {"q", ..., "q"}, and {"z", ..., "z"} is linearly independent, and its members combine to form Jordan chains. Finally, by the rank–nullity theorem, the cardinality of the union is "n". In other words, we have found a basis composed of Jordan chains, and this shows "A" can be put in Jordan normal form.


title: Jordan normal form

text: It can be shown that the Jordan normal form of a given matrix "A" is unique up to the order of the Jordan blocks.


title: Jordan normal form

text: Knowing the algebraic and geometric multiplicities of the eigenvalues is not sufficient to determine the Jordan normal form of "A". Assuming the algebraic multiplicity "m"("λ") of an eigenvalue "λ" is known, the structure of the Jordan form can be ascertained by analyzing the ranks of the powers ("A" − "λI"). To see this, suppose an "n" × "n" matrix "A" has only one eigenvalue "λ". So "m"("λ") = "n". The smallest integer "k" such that


title: Jordan normal form

text: is the size of the largest Jordan block in the Jordan form of "A". (This number "k" is also called the index of "λ". See discussion in a following section.) The rank of


title: Jordan normal form

text: is twice the number of Jordan blocks of size "k" plus the number of Jordan blocks of size "k" − 1. The general case is similar.


title: Jordan normal form

text: This can be used to show the uniqueness of the Jordan form. Let "J" and "J" be two Jordan normal forms of "A". Then "J" and "J" are similar and have the same spectrum, including algebraic multiplicities of the eigenvalues. The procedure outlined in the previous paragraph can be used to determine the structure of these matrices. Since the rank of a matrix is preserved by similarity transformation, there is a bijection between the Jordan blocks of "J" and "J". This proves the uniqueness part of the statement.


title: Jordan normal form

text: If "A" is a real matrix, its Jordan form can still be non-real. Instead of representing it with complex eigenvalues and 1's on the superdiagonal, as discussed above, there exists a real invertible matrix "P" such that "P""AP" = "J" is a real block diagonal matrix with each block being a real Jordan block. A real Jordan block is either identical to a complex Jordan block (if the corresponding eigenvalue formula_22 is real), or is a block matrix itself, consisting of 2×2 blocks (for non-real eigenvalue formula_44 with given algebraic multiplicity) of the form


title: Jordan normal form

text: and describe multiplication by formula_22 in the complex plane. The superdiagonal blocks are 2×2 identity matrices and hence in this representation the matrix dimensions are larger than the complex Jordan form. The full real Jordan block is given by


title: Jordan normal form

text: This real Jordan form is a consequence of the complex Jordan form. For a real matrix the nonreal eigenvectors and generalized eigenvectors can always be chosen to form complex conjugate pairs. Taking the real and imaginary part (linear combination of the vector and its conjugate), the matrix has this form with respect to the new basis.


title: Jordan normal form

text: Jordan reduction can be extended to any square matrix "M" whose entries lie in a field "K". The result states that any "M" can be written as a sum "D" + "N" where "D" is semisimple, "N" is nilpotent, and "DN" = "ND". This is called the Jordan–Chevalley decomposition. Whenever "K" contains the eigenvalues of "M", in particular when "K" is algebraically closed, the normal form can be expressed explicitly as the direct sum of Jordan blocks.


title: Jordan normal form

text: Similar to the case when "K" is the complex numbers, knowing the dimensions of the kernels of ("M" − "λI") for 1 ≤ "k" ≤ "m", where "m" is the algebraic multiplicity of the eigenvalue "λ", allows one to determine the Jordan form of "M". We may view the underlying vector space "V" as a "K"["x"]-module by regarding the action of "x" on "V" as application of "M" and extending by "K"-linearity. Then the polynomials ("x" − "λ") are the elementary divisors of "M", and the Jordan normal form is concerned with representing "M" in terms of blocks associated to the elementary divisors.


title: Jordan normal form

text: The proof of the Jordan normal form is usually carried out as an application to the ring "K"["x"] of the structure theorem for finitely generated modules over a principal ideal domain, of which it is a corollary.


title: Jordan normal form

text: One can see that the Jordan normal form is essentially a classification result for square matrices, and as such several important results from linear algebra can be viewed as its consequences.


title: Jordan normal form

text: Using the Jordan normal form, direct calculation gives a spectral mapping theorem for the polynomial functional calculus: Let "A" be an "n" × "n" matrix with eigenvalues "λ", ..., "λ", then for any polynomial "p", "p"("A") has eigenvalues "p"("λ"), ..., "p"("λ").


title: Jordan normal form

text: The characteristic polynomial of is formula_48. Similar matrices have the same characteristic polynomial.


title: Jordan normal form

text: where formula_22 is the "i"th root of formula_51 and formula_52 is its multiplicity, because this is clearly the characteristic polynomial of the Jordan form of "A".


title: Jordan normal form

text: The Cayley–Hamilton theorem asserts that every matrix "A" satisfies its characteristic equation: if is the characteristic polynomial of , then formula_53. This can be shown via direct calculation in the Jordan form, since if formula_22 is an eigenvalue of multiplicity formula_55,


title: Jordan normal form

text: As the diagonal blocks do not affect each other, the "i"th diagonal block of formula_58 is formula_57; hence formula_60.


title: Jordan normal form

text: The Jordan form can be assumed to exist over a field extending the base field of the matrix, for instance over the splitting field of ; this field extension does not change the matrix in any way.


title: Jordan normal form

text: The minimal polynomial P of a square matrix "A" is the unique monic polynomial of least degree, "m", such that "P"("A") = 0. Alternatively, the set of polynomials that annihilate a given "A" form an ideal "I" in "C"["x"], the principal ideal domain of polynomials with complex coefficients. The monic element that generates "I" is precisely "P".


title: Jordan normal form

text: Let "λ", …, "λ" be the distinct eigenvalues of "A", and "s" be the size of the largest Jordan block corresponding to "λ". It is clear from the Jordan normal form that the minimal polynomial of "A" has degree "s".


title: Jordan normal form

text: While the Jordan normal form determines the minimal polynomial, the converse is not true. This leads to the notion of elementary divisors. The elementary divisors of a square matrix "A" are the characteristic polynomials of its Jordan blocks. The factors of the minimal polynomial "m" are the elementary divisors of the largest degree corresponding to distinct eigenvalues.


title: Jordan normal form

text: The degree of an elementary divisor is the size of the corresponding Jordan block, therefore the dimension of the corresponding invariant subspace. If all elementary divisors are linear, "A" is diagonalizable.


title: Jordan normal form

text: The Jordan form of a "n" × "n" matrix "A" is block diagonal, and therefore gives a decomposition of the "n" dimensional Euclidean space into invariant subspaces of "A". Every Jordan block "J" corresponds to an invariant subspace "X". Symbolically, we put


title: Jordan normal form

text: where each "X" is the span of the corresponding Jordan chain, and "k" is the number of Jordan chains.


title: Jordan normal form

text: One can also obtain a slightly different decomposition via the Jordan form. Given an eigenvalue "λ", the size of its largest corresponding Jordan block "s" is called the index of "λ" and denoted by "v"("λ"). (Therefore, the degree of the minimal polynomial is the sum of all indices.) Define a subspace "Y" by


title: Jordan normal form

text: where "l" is the number of distinct eigenvalues of "A". Intuitively, we glob together the Jordan block invariant subspaces corresponding to the same eigenvalue. In the extreme case where "A" is a multiple of the identity matrix we have "k" = "n" and "l" = 1.


title: Jordan normal form

text: The projection onto "Y" and along all the other "Y" ( "j" ≠ "i" ) is called the spectral projection of "A" at v and is usually denoted by "P"("λ" ; "A"). Spectral projections are mutually orthogonal in the sense that "P"("λ" ; "A") "P"(v ; "A") = 0 if "i" ≠ "j". Also they commute with "A" and their sum is the identity matrix. Replacing every v in the Jordan matrix "J" by one and zeroing all other entries gives "P"(v ; "J"), moreover if "U J U" is the similarity transformation such that "A" = "U J U" then "P"("λ" ; "A") = "U P"("λ" ; "J") "U". They are not confined to finite dimensions. See below for their application to compact operators, and in holomorphic functional calculus for a more general discussion.


title: Jordan normal form

text: Comparing the two decompositions, notice that, in general, "l" ≤ "k". When "A" is normal, the subspaces "X"'s in the first decomposition are one-dimensional and mutually orthogonal. This is the spectral theorem for normal operators. The second decomposition generalizes more easily for general compact operators on Banach spaces.


title: Jordan normal form

text: It might be of interest here to note some properties of the index, "ν"("λ"). More generally, for a complex number "λ", its index can be defined as the least non-negative integer "ν"("λ") such that


title: Jordan normal form

text: So "ν"(v) > 0 if and only if "λ" is an eigenvalue of "A". In the finite-dimensional case, "ν"(v) ≤ the algebraic multiplicity of v.


title: Jordan normal form

text: The Jordan form is used to find a normal form of matrices up to conjugacy such that normal matrices make up an algebraic variety of a low fixed degree in the ambient matrix space.


title: Jordan normal form

text: Sets of representatives of matrix conjugacy classes for Jordan normal form or rational canonical forms in general do not constitute linear or


title: Jordan normal form

text: Find a canonical form of matrices over a field for which the set of representatives of matrix conjugacy classes is a union of affine linear subspaces (flats). In other words, map the set of matrix conjugacy classes injectively back into the initial set of matrices so that the image of this embedding—the set of all normal matrices, has the lowest possible degree—it is a union of shifted linear subspaces.


title: Jordan normal form

text: The construction of a uniquely defined plane normal form of a matrix starts by considering its Jordan normal form.


title: Jordan normal form

text: Iteration of the Jordan chain motivates various extensions to more abstract settings. For finite matrices, one gets matrix functions; this can be extended to compact operators and the holomorphic functional calculus, as described further below.


title: Jordan normal form

text: The Jordan normal form is the most convenient for computation of the matrix functions (though it may be not the best choice for computer computations). Let "f"("z") be an analytical function of a complex argument. Applying the function on a "n"×"n" Jordan block "J" with eigenvalue "λ" results in an upper triangular matrix:


title: Jordan normal form

text: so that the elements of the "k"-th superdiagonal of the resulting matrix are formula_66. For a matrix of general Jordan normal form the above expression shall be applied to each Jordan block.


title: Jordan normal form

text: where the binomial coefficients are defined as formula_68. For integer positive "n" it reduces to standard definition


title: Jordan normal form

text: A result analogous to the Jordan normal form holds for compact operators on a Banach space. One restricts to compact operators because every point "x" in the spectrum of a compact operator "T" is an eigenvalue; The only exception is when "x" is the limit point of the spectrum. This is not true for bounded operators in general. To give some idea of this generalization, we first reformulate the Jordan decomposition in the language of functional analysis.


title: Jordan normal form

text: Let "X" be a Banach space, "L"("X") be the bounded operators on "X", and "σ"("T") denote the spectrum of "T" ∈ "L"("X"). The holomorphic functional calculus is defined as follows:


title: Jordan normal form

text: Fix a bounded operator "T". Consider the family Hol("T") of complex functions that is holomorphic on some open set "G" containing "σ"("T"). Let Γ = {"γ"} be a finite collection of Jordan curves such that "σ"("T") lies in the "inside" of Γ, we define "f"("T") by


title: Jordan normal form

text: The open set "G" could vary with "f" and need not be connected. The integral is defined as the limit of the Riemann sums, as in the scalar case. Although the integral makes sense for continuous "f", we restrict to holomorphic functions to apply the machinery from classical function theory (for example, the Cauchy integral formula). The assumption that "σ"("T") lie in the inside of Γ ensures "f"("T") is well defined; it does not depend on the choice of Γ. The functional calculus is the mapping Φ from Hol("T") to "L"("X") given by


title: Jordan normal form

text: In the finite-dimensional case, "σ"("T") = {"λ"} is a finite discrete set in the complex plane. Let "e" be the function that is 1 in some open neighborhood of "λ" and 0 elsewhere. By property 3 of the functional calculus, the operator


title: Jordan normal form

text: has spectrum {0}. By property 1, "f"("T") can be directly computed in the Jordan form, and by inspection, we see that the operator "f"("T")"e"("T") is the zero matrix.


title: Jordan normal form

text: By property 3, "f"("T") "e"("T") = "e"("T") "f"("T"). So "e"("T") is precisely the projection onto the subspace


title: Jordan normal form

text: where the index "i" runs through the distinct eigenvalues of "T". This is the invariant subspace decomposition


title: Jordan normal form

text: given in a previous section. Each "e"("T") is the projection onto the subspace spanned by the Jordan chains corresponding to "λ" and along the subspaces spanned by the Jordan chains corresponding to v for "j" ≠ "i". In other words, "e"("T") = "P"("λ";"T"). This explicit identification of the operators "e"("T") in turn gives an explicit form of holomorphic functional calculus for matrices:


title: Jordan normal form

text: Notice that the expression of "f"("T") is a finite sum because, on each neighborhood of v, we have chosen the Taylor series expansion of "f" centered at v.


title: Jordan normal form

text: Let "T" be a bounded operator "λ" be an isolated point of "σ"("T"). (As stated above, when "T" is compact, every point in its spectrum is an isolated point, except possibly the limit point 0.)


title: Jordan normal form

text: The point "λ" is called a pole of operator "T" with order "ν" if the resolvent function "R" defined by


title: Jordan normal form

text: We will show that, in the finite-dimensional case, the order of an eigenvalue coincides with its index. The result also holds for compact operators.


title: Jordan normal form

text: Consider the annular region "A" centered at the eigenvalue "λ" with sufficiently small radius "ε" such that the intersection of the open disc "B"("λ") and "σ"("T") is {"λ"}. The resolvent function "R" is holomorphic on "A".


title: Jordan normal form

text: is precisely the index of "λ", "ν"("λ"). In other words, the function "R" has a pole of order "ν"("λ") at "λ".


title: Jordan normal form

text: If the matrix "A" has multiple eigenvalues, or is close to a matrix with multiple eigenvalues, then its Jordan normal form is very sensitive to perturbations. Consider for instance the matrix


title: Jordan normal form

text: This ill conditioning makes it very hard to develop a robust numerical algorithm for the Jordan normal form, as the result depends critically on whether two eigenvalues are deemed to be equal. For this reason, the Jordan normal form is usually avoided in numerical analysis; the stable Schur decomposition or pseudospectra are better alternatives.


title: Assassins (1995 film)

text: Assassins is a 1995 American action thriller film directed by Richard Donner. The screenplay was written by The Wachowskis and Brian Helgeland. The film stars Sylvester Stallone and Antonio Banderas and costars Julianne Moore. The Wachowskis stated that their script was completely rewritten by Helgeland, and that they tried to remove their names from the film but failed.


title: Assassins (1995 film)

text: Assassin Robert Rath (Sylvester Stallone) plans to retire, haunted by the memory of murdering his mentor Nicolai several years ago. While on an assignment, Miguel Bain (Antonio Banderas), another assassin, manages to eliminate Rath’s target first. Bain then reveals his plan to kill Rath and become the world’s best assassin.


title: Assassins (1995 film)

text: As Rath tries to figure out who sent Bain, his contractor offers him a lucrative job that could allow him to retire: kill a computer hacker named Electra (Julianne Moore), the four Dutch buyers of a computer disk she possesses, and to retrieve the disk. Electra has set up CCTV cameras and an elaborate mechanism for remotely moving items between rooms in the building where she is based.


title: Assassins (1995 film)

text: Bain finds and kills the four Dutch buyers first, who he discovers to be Interpol agents. Rath, meanwhile spares Electra, and the two escape from Bain with the disk. Rath exchanges the disk for his fee, given to him in a briefcase, which contains a bomb placed by his contractor in an attempt to kill him. Electra then tells him she had swapped the disk, unsure if Rath would come back. Rath demands a greatly increased fee from his contractor, this time to be wired to a bank.


title: Assassins (1995 film)

text: The contractor then hires Bain to kill Rath. Rath and Electra travel to the bank in Puerto Rico, where Rath identifies the decrepit, abandoned hotel that Bain will use as a sniper post and plans a trap.


title: Assassins (1995 film)

text: After Bain's apparent death, Nicolai appears, revealing that he had had a bulletproof vest on when Rath shot him. Knowing that Nicolai would kill him too, Bain joins Rath in shooting him dead. Bain still plans to kill Rath and become number one. Electra puts on her sunglasses, allowing Rath to see Bain; Rath shoots through his jacket to kill him. After Bain's death, Rath and Electra leave the place, take Electra's cat and say that their true names are Joseph and Anna respectively.


title: Assassins (1995 film)

text: The original spec screenplay was written by The Wachowskis and sold for $1 million to producer Joel Silver around the same time he bought their script for "The Matrix", also for $1 million. The script was similar to the final product, but with a more developed love story between Rath and Electra and a briefer ending without the character of Nicolai. Joel Silver offered Richard Donner $10 million to direct, but Donner insisted the script be rewritten to tone down the violence and make the central character more sympathetic and brought in Brian Helgeland, who did a page one rewrite and earned a co-screenwriter credit. The Wachowskis attempted to remove their name from the film but were refused by the Writers Guild of America.


title: Assassins (1995 film)

text: The film received mostly negative press, and on the film-critic aggregator Rotten Tomatoes received 16% positive reviews based on 50 reviews, with an average rating of 3.71/10. The script was heavily criticized for being confusing and dull. Stallone's performance in the film earned him a Golden Raspberry Award nomination for Worst Actor (also for "Judge Dredd"), but lost the trophy to Pauly Shore for "Jury Duty".


title: Assassins (1995 film)

text: About the reception, Richard Donner said: ""Assassins", I thought Stallone did one of the best jobs he's ever done. He underplayed, he was quiet, he found the character and he went with it. I thought Antonio Banderas was wonderful. The picture came out, and it did not do very well at all. Sure, it hurts and you know why you wish it would do better? The studio gave you a lot of money and you want them to make their money back so that other people can make movies. When we made "The Omen", that money Alan Ladd was able to spend at Fox to do "Star Wars". So you feel good about that. Not only is your picture a success, but it helps other people too. Warners have been good to us and gave us money to make that movie. And I thought we did a good job and they thought we did a good job, but the audiences and critics didn't like it. Did I feel bad? Sure. Did it get me down? Nope, nope, nope — too lucky to be in this business to be down in the dumps."


title: Assassins (1995 film)

text: "Assassins" debuted at No. 2 at the box office. The film grossed $30.3 million in the US and another $53 million worldwide, for a total of $83.3 million.


title: Troma Entertainment

text: Troma Entertainment is an American independent film production and distribution company founded by Lloyd Kaufman and Michael Herz in 1974. The company produces low-budget independent films, primarily of the horror comedy genre. Many of them play on 1950s horror with elements of farce, parody, gore and splatter.


title: Troma Entertainment

text: In 2012, the company officially released many of its films on YouTube. However, their YouTube channel was eventually terminated for not meeting community standards.


title: Troma Entertainment

text: Troma has produced, acquired and distributed over 1,000 independent films since its creation. Its slogan in 2014 was "40 years of Disrupting Media". Another slogan the company has used is "Movies of the Future." The company also has its own streaming service called Troma Now.


title: Troma Entertainment

text: Troma films are B-movies known for their surrealistic or automatistic nature, along with their use of shocking imagery; some would categorize them as "shock exploitation films". They typically contain overt sexuality, nudity, and intentionally sadistic, gory, and blatant graphic violence, so much that "Troma film" has become a term synonymous with these characteristics. Troma reuses the same props, actors, and scenes repeatedly, sometimes to save money. At a certain point, however, this became another hallmark of Troma. Examples include a severed leg, a penis monster, and the flipping and exploding car filmed for the movie "Sgt. Kabukiman N.Y.P.D.", which is used in place of any other car that needs to crash and explode.


title: Troma Entertainment

text: Troma produced or acquired early films featuring several rising talents, such as Carmen Electra (""), Billy Bob Thornton ("Chopper Chicks in Zombietown"), Vanna White ("Graduation Day"), Kevin Costner ("Sizzle Beach, U.S.A."), J. J. Abrams ("Nightbeast"), Samuel L. Jackson ("Def by Temptation"), Marisa Tomei ("The Toxic Avenger"), Michael Jai White ("The Toxic Avenger Part II"), Vincent D'Onofrio ("The First Turn-On!"), David Boreanaz ("Macabre Pair of Shorts"), Paul Sorvino ("Cry Uncle!"), James Gunn ("Tromeo and Juliet"), Trey Parker and Matt Stone ("Cannibal! The Musical"), before they were discovered. Another Academy Award-winning director, Oliver Stone, made his debut as an actor in "The Battle of Love's Return".


title: Troma Entertainment

text: In the mid-1970s, Kaufman and Herz began producing, directing, and distributing raunchy sex comedies such as "The First Turn-On!" and "Squeeze Play!". Troma provided production support for Louis Malle's "My Dinner With Andre", for which Kaufman served as a production manager.


title: Troma Entertainment

text: In 1985, Troma had a hit with the violent comedy horror superhero film "The Toxic Avenger". The film went on to become Troma's most popular, spawning sequels and an animated television program. However, following the financial demise of the company Troma itself, the sequels to the film were box office bombs, and the cartoon adaptation quickly ended. The Toxic Avenger character is now Troma's official mascot.


title: Troma Entertainment

text: Kaufman's follow-up film to "The Toxic Avenger" was "Class of Nuke 'Em High", co-directed with Richard W. Haines. The film was a hit nearly as successful, though it inspired two unsuccessful sequels, both following the financial demise of Troma. At one time, it was the highest-selling VHS release for Troma.


title: Troma Entertainment

text: "The Toxic Avenger" was turned into a musical which debuted at the George Street Playhouse in New Brunswick, New Jersey and opened in New York in the fall of 2008. "The Toxic Avenger Musical" book by Joe DiPietro, the author of the long-running "I Love You, You're Perfect, Now Change" and "All Shook Up", was released the same year. The music is by David Bryan, keyboardist of the rock band Bon Jovi.


title: Troma Entertainment

text: Soon after "Class of Nuke 'Em High" was completed and distributed, Kaufman directed "Troma's War". Intended as a criticism of what it saw as Ronald Reagan's attempt to glamorize war, the story concerns a group of everyday people who crash land on a remote island, only to find it populated by an isolationist militia that intends to overthrow the US government. "Troma's War" was a box office bomb. In the aftermath of the film's poor performance, despite another stab at the superhero genre with "Sgt. Kabukiman N.Y.P.D.", Troma experienced financial hardship and tried to reestablish itself as a smaller company mostly out of necessity.


title: Troma Entertainment

text: Today, the majority of Troma films are viewed for the first time on VHS or DVD, with some theatrical releases for their films in smaller art houses, college campuses, and independent cinemas.


title: Troma Entertainment

text: From 1995 to 2000, Troma had a period of creativity and produced some of their greatest work. Kaufman directed three independent films, all distributed in limited theatrical releases: "Tromeo and Juliet", a loose parody of Shakespeare's play; "Terror Firmer", a slasher film loosely based on Kaufman's book "All I Need to Know about Filmmaking I Learned from The Toxic Avenger", and an independent film sequel to "The Toxic Avenger" trilogy titled "".


title: Troma Entertainment

text: Troma's financial hardship worsened after the botched funding of a low-budget video feature titled "Tales from the Crapper", which cost $250,000 despite most of the footage being completely unusable. India Allen, one of the producers, backed out of the film halfway through, and sued Troma, citing breach of contract, slander, sexual harassment, trade slander, and intentional infliction of emotional distress. Kaufman supervised a reshoot in an attempt to salvage the film, dividing the footage into two parts and recasting the film as a double feature. "Tales from the Crapper" was released on DVD in September 2004.


title: Troma Entertainment

text: Currently, Troma produces and acquires independent films, despite financial hardships and limitations. Troma Films has distributed many films from third parties including Trey Parker's "Cannibal! The Musical". Lloyd encourages independent filmmaking, making cameo appearances in many low-budget horror films, occasionally without fee. Among his more recent appearances is in former collaborator James Gunn's directing debut, "Slither", and "Guardians of the Galaxy".


title: Troma Entertainment

text: Kaufman's long-time editor Gabriel Friedman co-directed and wrote the screenplay to his follow-up film, "Poultrygeist: Night of the Chicken Dead", a musical zom-com which made its official New York premiere on May 9, 2008 (although the film had previewed numerous times on single screens for over a year). The film opened to positive reviews from "Entertainment Weekly" and "The New York Times" and was released in 2006 in theaters and in 2008 on DVD.


title: Troma Entertainment

text: During the winter of 2010/2011, Troma produced a feature-length film "Father's Day", which Kaufman calls "a response film to Mother's Day". The film was written and directed by the Canadian filmmaking team Astron-6, debuting October 21, 2011, at the Toronto After Dark Film Festival where it took home the top prize of BEST FILM, as well as five other awards. In 2012 "Father's Day" was featured on the cover of Rue Morgue magazine and won Best Feature Film, Best Director, Best Male Performance, and Best Special Effects at The Fantastic Planet/A Night of Horror International film festival. This is rare for a film that cost only ten thousand dollars to make. On October 31, 2012, "Father's Day" was refused classification in Australia, which makes it effectively illegal to sell or exhibit the film. A second censored version was eventually passed with an R18+ rating.


title: Troma Entertainment

text: In August 2012, Troma released over 100 of its back catalog films on YouTube, many for free, some for 48-hour paid viewing. However, their YouTube channel was terminated in 2020 for not meeting community standards. This occurred after YouTube received several complaints about the channel.


title: Troma Entertainment

text: On April 7, 2010, Kaufman confirmed that a PG-13 remake of "The Toxic Avenger" was happening and will be produced by Akiva Goldsman. It actually is not the first attempt at a general audience-friendly version of the franchise, as "Make Your Own Damn Movie" noted a prior deal with New Line in the early 90s for a live-action take on the Toxic Crusaders. Another 1980s Troma classic, "Mother's Day" will also receive a remake and will be directed by Darren Lynn Bousman and produced by Brett Ratner. At the time Kaufman also said that he was negotiating a deal for a remake of "Class of Nuke 'Em High". Shortly after, Troma and Starz Entertainment entered into agreement for the production of "Return to Nuke Em High" as a two-volume title. The first volume was released in theaters and on home video. The second volume, delayed due to funding issues, was stated on its Kickstarter website in January 2017 to be nearing completion.


title: Troma Entertainment

text: In 2015, Troma launched a streaming service called Troma Now, which offers many of the films distributed by Troma to subscribers. The service offers subscribers a free trial month, after which they will need to pay a monthly price of $4.99.


title: Troma Entertainment

text: Troma holds an annual Tromadance Festival, originally taking place in Park City, Utah at the same time as the Sundance Festival to accentuate their true independence from the mainstream. The festival screens submitted movies from independent filmmakers from around the world, the best of which are usually released on DVD by Troma or compiled in the Best of Tromadance series. In parallel, Troma acts as adviser to aspiring filmmakers with Kaufman teaching classes, contributing cameos and often releasing the finished films on DVD.


title: Troma Entertainment

text: 2009 marked the last time Tromadance was held in Utah; the festival was subsequently relocated to Asbury Park, New Jersey. In 2014, the festival moved to New York City and took place in June.


title: Troma Entertainment

text: Kaufman has also had some success with several non-fiction books and a novelization of "The Toxic Avenger". Released in 1998, "All I Need to Know about Filmmaking I Learned from The Toxic Avenger" is an autobiography of sorts co-written with James Gunn. This book chronicles the history of the company, its films, and its iconic figurehead. Kaufman continued to draw on his experiences as Troma chief in the "how-to" filmmaking books "Make Your Own Damn Movie!", "Direct Your Own Damn Movie!", "Produce Your Own Damn Movie!" and "Sell Your Own Damn Movie!". A DVD box set has been released to coincide with release of each of the first three books. In the video series, Kaufman interviews famous and infamous filmmakers about various filmmaking subjects.


title: Troma Entertainment

text: In 2006, a novelization of "The Toxic Avenger" was released. It was co-written by Kaufman and long-time Troma employee Adam Jahnke.


title: Troma Entertainment

text: Also see List of Troma Team Video titles for a complete list of films distributed by Troma Entertainment. Below is a list of some Troma distributed films.


title: Troma Entertainment

text: Some titles which have at one time, or another, been distributed by Troma Inc. have left the catalog. For instance, "My Neighbor Totoro" was originally released by Troma's subsidiary 50th Street Films, but only for a short time, and only for U.S. theatrical release. Others were briefly licensed for distribution on VHS such as "Femme Fontaine Killer Babe for the C.I.A." which was one of Troma Team Video's original launch titles along with "Sgt. Kabukiman N.Y.P.D." and "Class of Nuke 'em High Part III: The Good, The Bad and The Subhumanoid". Some titles, such as "Maniac Nurses Find Ecstasy", are included on this list because they were previously listed but no longer appear in Troma's catalog.


title: Troma Entertainment

text: Most of the films made by Troma Entertainment take place in the fictional New Jersey city of Tromaville, known as the "Toxic Chemical Capital of the World." Examples include the "Toxic Avenger" films and the "Class of Nuke 'Em High" films. Another film worth mentioning takes place in a post-apocalyptic Tromaville titled "A Nymphoid Barbarian In Dinosaur Hell". The following is a list of films that either take place in, or mention, Tromaville.


title: Mercedes-Benz OM642 engine

text: The Mercedes-Benz OM642 engine is a , 24-valve, aluminium/aluminium block and heads diesel 72° V6 engine manufactured by the Mercedes-Benz division of Daimler AG as a replacement for the Mercedes straight-5 and straight-6 cylinder engines.


title: Mercedes-Benz OM642 engine

text: The engine features common rail Direct injection and a variable nozzle turbocharger. The injection system operates at , while the compression ratio is 18.0:1. The engine features a counter-rotating balance shaft mounted between the cylinder banks to cancel the vibrations inherent to the 72 degree V6 design, and the crankpins are offset by 48 degrees to achieve even 120 degree firing intervals. In some heavy vehicle applications, Mercedes' BlueTec AdBlue urea injection is utilised for NOx reduction. In lighter vehicle applications, a NOx storage catalyst captures nitrous oxides, which are periodically purged (decomposed) by running the engine slightly rich. A particulate filter lowers soot, making this engine ULEV certified. Engine mass is . Power output is and of torque. For the 2007 model year, torque is raised to .


title: Mercedes-Benz OM642 engine

text: At the beginning of summer 2017 the engine, together with Mercedes-Benz OM651 was under investigation by the Federal Motor Transport Authority in respect of the alleged emissions cheating scandal wherein the laboratory emissions testing produced a different amount of diesel exhaust fluid usage and lower emissions than in real world operating scenarios.


title: Mercedes-Benz OM642 engine

text: Air is drawn into the engine through two air filters located above each cylinder head. The amount of the air is measured by two hot film mass air flow sensors B2/6&7. On Sprinter models, a single air filter housing is mounted upon brackets on top of the engine.


title: Mercedes-Benz OM642 engine

text: The variable geometry Turbine is actuated via a linkage connecting the controller to vanes inside the Turbine housing. In the full-boost position, air is allowed to pass over the Turbine impeller. In the no boost position the vanes block exhaust gasses from acting on the impeller and route them down the exhaust pipe.


title: Angie Cepeda

text: Angélica María Cepeda Jiménez (born 2 August 1974), professionally known as Angie Cepeda, is a Colombian actress. She is best known for her roles in the telenovela "Pobre Diabla" and the films "Captain Pantoja and the Special Services" and "Love in the Time of Cholera". She is the younger sister of actress Lorna Paz.


title: Angie Cepeda

text: Cepeda was born in Cartagena de Indias, Colombia, and raised in Barranquilla. After her parents divorced she lived with her mother and two older sisters (one of whom is actress Lorna Paz).


title: Angie Cepeda

text: When she discovered her vocation in drama, she moved out to Bogotá. After starting her drama courses, she was contracted by a beer company and made some advertisements for it. Next, she played some bit parts in several soap operas and movies in Colombia.


title: Angie Cepeda

text: Cepeda got a role in the soap opera "Las Juanas", getting the attention of some TV producers who offered her jobs in prime time shows, such as the leading role in "Luz Maria" (1998), co-starring Christian Meier and Rosalinda Serfaty, and that as Fiorella Morelli Flores de Mejía Guzmán in "Pobre Diabla" (2000), opposite Salvador del Solar and Santiago Magill.


title: Angie Cepeda

text: In the cinematic world, Peruvian director Francisco Lombardi convinced her to portray a prostitute called "La Colombiana" in "Pantaleón y las Visitadoras" (released in English as "Captain Pantoja and the Special Services"). In 2021, she voiced Julieta Madrigal in the English, Spanish and Italian language versions of the Disney animated musical film "Encanto".


title: Moment magnitude scale

text: The moment magnitude scale (MMS; denoted explicitly with or Mw, and generally implied with use of a single M for magnitude) is a measure of an earthquake's magnitude ("size" or strength) based on its seismic moment. It was defined in a 1979 paper by Thomas C. Hanks and Hiroo Kanamori. Similar to the local magnitude scale () defined by Charles Francis Richter in 1935, it uses a logarithmic scale; small earthquakes have approximately the same magnitudes on both scales.


title: Moment magnitude scale

text: Moment magnitude () is considered the authoritative magnitude scale for ranking earthquakes by size. It is more directly related to the energy of an earthquake than other scales, and does not saturate—that is, it does not underestimate magnitudes as other scales do in certain conditions. It has become the standard scale used by seismological authorities like the U.S. Geological Survey for reporting large earthquakes (typically M > 4), replacing the local magnitude () and surface wave magnitude () scales. Subtypes of the moment magnitude scale (, etc.) reflect different ways of estimating the seismic moment.


title: Moment magnitude scale

text: At the beginning of the twentieth century, very little was known about how earthquakes happen, how seismic waves are generated and propagate through the earth's crust, and what information they carry about the earthquake rupture process; the first magnitude scales were therefore empirical. The initial step in determining earthquake magnitudes empirically came in 1931 when the Japanese seismologist Kiyoo Wadati showed that the maximum amplitude of an earthquake's seismic waves diminished with distance at a certain rate. Charles F. Richter then worked out how to adjust for epicentral distance (and some other factors) so that the logarithm of the amplitude of the seismograph trace could be used as a measure of "magnitude" that was internally consistent and corresponded roughly with estimates of an earthquake's energy. He established a reference point and the now familiar ten-fold (exponential) scaling of each degree of magnitude, and in 1935 published what he called the "magnitude scale", now called the local magnitude scale, labeled . (This scale is also known as the "Richter scale", but news media sometimes use that term indiscriminately to refer to other similar scales.)


title: Moment magnitude scale

text: The local magnitude scale was developed on the basis of shallow (~ deep), moderate-sized earthquakes at a distance of approximately , conditions where the surface waves are predominant. At greater depths, distances, or magnitudes the surface waves are greatly reduced, and the local magnitude scale underestimates the magnitude, a problem called "saturation". Additional scales were developed – a surface-wave magnitude scale () by Beno Gutenberg in 1945, a body-wave magnitude scale () by Gutenberg and Richter in 1956, and a number of variants – to overcome the deficiencies of the scale, but all are subject to saturation. A particular problem was that the scale (which in the 1970s was the preferred magnitude scale) saturates around and therefore underestimates the energy release of "great" earthquakes such as the 1960 Chilean and 1964 Alaskan earthquakes. These had magnitudes of 8.5 and 8.4 respectively but were notably more powerful than other M 8 earthquakes; their moment magnitudes were closer to 9.6 and 9.3.


title: Moment magnitude scale

text: The study of earthquakes is challenging as the source events cannot be observed directly, and it took many years to develop the mathematics for understanding what the seismic waves from an earthquake can tell us about the source event. An early step was to determine how different systems of forces might generate seismic waves equivalent to those observed from earthquakes.


title: Moment magnitude scale

text: The simplest force system is a single force acting on an object. If it has sufficient strength to overcome any resistance it will cause the object to move ("translate"). A pair of forces, acting on the same "line of action" but in opposite directions, will cancel; if they cancel (balance) exactly there will be no net translation, though the object will experience stress, either tension or compression. If the pair of forces are offset, acting along parallel but separate lines of action, the object experiences a rotational force, or torque. In mechanics (the branch of physics concerned with the interactions of forces) this model is called a "couple", also "simple couple" or "single couple". If a second couple of equal and opposite magnitude is applied their torques cancel; this is called a "double couple". A double couple can be viewed as "equivalent to a pressure and tension acting simultaneously at right angles".


title: Moment magnitude scale

text: In 1923 Hiroshi Nakano showed that certain aspects of seismic waves could be explained in terms of a double couple model. This led to a three-decade long controversy over the best way to model the seismic source: as a single couple, or a double couple. While Japanese seismologists favored the double couple, most seismologists favored the single couple. Although the single couple model had some short-comings, it seemed more intuitive, and there was a belief – mistaken, as it turned out – that the elastic rebound theory for explaining why earthquakes happen required a single couple model. In principle these models could be distinguished by differences in the radiation patterns of their S-waves, but the quality of the observational data was inadequate for that.


title: Moment magnitude scale

text: A double couple model suffices to explain an earthquake's far-field pattern of seismic radiation, but tells us very little about the nature of an earthquake's source mechanism or its physical features. While slippage along a fault was theorized as the cause of earthquakes (other theories included movement of magma, or sudden changes of volume due to phase changes), observing this at depth was not possible, and understanding what could be learned about the source mechanism from the seismic waves requires an understanding of the source mechanism.


title: Moment magnitude scale

text: Modeling the physical process by which an earthquake generates seismic waves required much theoretical development of dislocation theory, first formulated by the Italian Vito Volterra in 1907, with further developments by E. H. Love in 1927. More generally applied to problems of stress in materials, an extension by F. Nabarro in 1951 was recognized by the Russian geophysicist A. V. Vvedenskaya as applicable to earthquake faulting. In a series of papers starting in 1956 she and other colleagues used dislocation theory to determine part of an earthquake's focal mechanism, and to show that a dislocation – a rupture accompanied by slipping — was indeed equivalent to a double couple.


title: Moment magnitude scale

text: In a pair of papers in 1958, J. A. Steketee worked out how to relate dislocation theory to geophysical features. Numerous other researchers worked out other details, culminating in a general solution in 1964 by Burridge and Knopoff, which established the relationship between double couples and the theory of elastic rebound, and provided the basis for relating an earthquake's physical features to seismic moment.


title: Moment magnitude scale

text: "Seismic moment" – symbol – is a measure of the fault slip and area involved in the earthquake. Its value is the torque of each of the two force couples that form the earthquake's equivalent double-couple. (More precisely, it is the scalar magnitude of the second-order moment tensor that describes the force components of the double-couple.) Seismic moment is measured in units of Newton meters (N·m) or Joules, or (in the older CGS system) dyne-centimeters (dyn-cm).


title: Moment magnitude scale

text: The first calculation of an earthquake's seismic moment from its seismic waves was by Keiiti Aki for the 1964 Niigata earthquake. He did this two ways. First, he used data from distant stations of the WWSSN to analyze long-period (200 second) seismic waves (wavelength of about 1,000 kilometers) to determine the magnitude of the earthquake's equivalent double couple. Second, he drew upon the work of Burridge and Knopoff on dislocation to determine the amount of slip, the energy released, and the stress drop (essentially how much of the potential energy was released). In particular, he derived a now famous equation that relates an earthquake's seismic moment to its physical parameters:


title: Moment magnitude scale

text: with being the rigidity (or resistance to moving) of a fault with a surface area of over an average dislocation (distance) of . (Modern formulations replace with the equivalent , known as the "geometric moment" or "potency".) By this equation the "moment" determined from the double couple of the seismic waves can be related to the moment calculated from knowledge of the surface area of fault slippage and the amount of slip. In the case of the Niigata earthquake the dislocation estimated from the seismic moment reasonably approximated the observed dislocation.


title: Moment magnitude scale

text: Seismic moment is a measure of the work (more precisely, the torque) that results in inelastic (permanent) displacement or distortion of the earth's crust. It is related to the total energy released by an earthquake. However, the power or potential destructiveness of an earthquake depends (among other factors) on how much of the total energy is converted into seismic waves. This is typically 10% or less of the total energy, the rest being expended in fracturing rock or overcoming friction (generating heat).


title: Moment magnitude scale

text: Nonetheless, seismic moment is regarded as the fundamental measure of earthquake size, representing more directly than other parameters the physical size of an earthquake. As early as 1975 it was considered "one of the most reliably determined instrumental earthquake source parameters".


title: Moment magnitude scale

text: Most earthquake magnitude scales suffered from the fact that they only provided a comparison of the amplitude of waves produced at a standard distance and frequency band; it was difficult to relate these magnitudes to a physical property of the earthquake. Gutenberg and Richter suggested that radiated energy E could be estimated as


title: Moment magnitude scale

text: (in Joules). Unfortunately, the duration of many very large earthquakes was longer than 20 seconds, the period of the surface waves used in the measurement of . This meant that giant earthquakes such as the 1960 Chilean earthquake (M 9.5) were only assigned an . Caltech seismologist Hiroo Kanamori recognized this deficiency and took the simple but important step of defining a magnitude based on estimates of radiated energy, , where the "w" stood for work (energy):


title: Moment magnitude scale

text: Kanamori recognized that measurement of radiated energy is technically difficult since it involves the integration of wave energy over the entire frequency band. To simplify this calculation, he noted that the lowest frequency parts of the spectrum can often be used to estimate the rest of the spectrum. The lowest frequency asymptote of a seismic spectrum is characterized by the seismic moment, . Using an approximate relation between radiated energy and seismic moment (which assumes stress drop is complete and ignores fracture energy),


title: Moment magnitude scale

text: The formula above made it much easier to estimate the energy-based magnitude , but it changed the fundamental nature of the scale into a moment magnitude scale. USGS seismologist Thomas C. Hanks noted that Kanamori's scale was very similar to a relationship between and that was reported by


title: Moment magnitude scale

text: Moment magnitude is now the most common measure of earthquake size for medium to large earthquake magnitudes, but in practice, seismic moment (), the seismological parameter it is based on, is not measured routinely for smaller quakes. For example, the United States Geological Survey does not use this scale for earthquakes with a magnitude of less than 3.5, which includes the great majority of quakes.


title: Moment magnitude scale

text: Popular press reports most often deal with significant earthquakes larger than . For these events, the preferred magnitude is the moment magnitude , not Richter's local magnitude .


title: Moment magnitude scale

text: The symbol for the moment magnitude scale is , with the subscript "w" meaning mechanical work accomplished. The moment magnitude is a dimensionless value defined by Hiroo Kanamori as


title: Moment magnitude scale

text: where is the seismic moment in dyne⋅cm (10 N⋅m). The constant values in the equation are chosen to achieve consistency with the magnitude values produced by earlier scales, such as the local magnitude and the surface wave magnitude. Thus, a magnitude zero microearthquake has a seismic moment of approximately , while the Great Chilean earthquake of 1960, with an estimated moment magnitude of 9.4–9.6, had a seismic moment between and .


title: Moment magnitude scale

text: Seismic moment is not a direct measure of energy changes during an earthquake. The relations between seismic moment and the energies involved in an earthquake depend on parameters that have large uncertainties and that may vary between earthquakes. Potential energy is stored in the crust in the form of elastic energy due to built-up stress and gravitational energy. During an earthquake, a portion formula_10 of this stored energy is transformed into


title: Moment magnitude scale

text: where formula_15 is the average of the "absolute" shear stresses on the fault before and after the earthquake (e.g., equation 3 of ) and formula_16 is the average of the shear moduli of the rocks that constitute the fault. Currently, there is no technology to measure absolute stresses at all depths of interest, nor method to estimate it accurately, and formula_15 is thus poorly known. It could vary highly from one earthquake to another. Two earthquakes with identical formula_18 but different formula_15 would have released different formula_10.


title: Moment magnitude scale

text: where formula_22 is radiated efficiency and formula_23 is the static stress drop, i.e., the difference between shear stresses on the fault before and after the earthquake (e.g., from equation 1 of ). These two quantities are far from being constants. For instance, formula_24 depends on rupture speed; it is close to 1 for regular earthquakes but much smaller for slower earthquakes such as tsunami earthquakes and slow earthquakes. Two earthquakes with identical formula_18 but different formula_24 or formula_23 would have radiated different formula_28.


title: Moment magnitude scale

text: Because formula_28 and formula_18 are fundamentally independent properties of an earthquake source, and since formula_28 can now be computed more directly and robustly than in the 1970s, introducing a separate magnitude associated to radiated energy was warranted. Choy and Boatwright defined in 1995 the "energy magnitude"


title: Moment magnitude scale

text: Assuming the values of are the same for all earthquakes, one can consider as a measure of the potential energy change Δ"W" caused by earthquakes. Similarly, if one assumes formula_34 is the same for all earthquakes, one can consider as a measure of the energy "E" radiated by earthquakes.


title: Moment magnitude scale

text: Under these assumptions, the following formula, obtained by solving for the equation defining , allows one to assess the ratio formula_35 of energy release (potential or radiated) between two earthquakes of different moment magnitudes, formula_36 and formula_37:


title: Moment magnitude scale

text: As with the Richter scale, an increase of one step on the logarithmic scale of moment magnitude corresponds to a 10 ≈ 32 times increase in the amount of energy released, and an increase of two steps corresponds to a 10 = 1000 times increase in energy. Thus, an earthquake of of 7.0 contains 1000 times as much energy as one of 5.0 and about 32 times that of 6.0.


title: Moment magnitude scale

text: To make the significance of the magnitude value plausible, the seismic energy released during the earthquake is sometimes compared to the effect of the conventional chemical explosive TNT.


title: Moment magnitude scale

text: The seismic energy formula_39 results from the above mentioned formula according to Gutenberg and Richter to


title: Moment magnitude scale

text: For comparison of seismic energy (in joules) with the corresponding explosion energy, a value of 4.2 - 10 joules per ton of TNT applies.


title: Moment magnitude scale

text: The end of the scale is at the value 10.6 corresponding to the assumption that at this value the earth's crust would have to break apart completely.


title: Moment magnitude scale

text: Various ways of determining moment magnitude have been developed, and several subtypes of the scale can be used to indicate the basis used.


title: Sara Vickers

text: Sara Louise Vickers (born 1985) is a British theatre, television and film actress best known for playing Joan Thursday in the British television detective drama series "Endeavour".


title: Sara Vickers

text: Vickers was born in 1985, in Strathaven, Scotland, and grew up in Edinburgh. She graduated with a BA from the Royal Academy of Dramatic Art in 2010.


title: Sara Vickers

text: In 2010 Vickers appeared in Ibsen's "The Lady from the Sea", adapted by David Eldridge and directed by Sarah Frankcom at the Royal Exchange Theatre, Manchester. Playing Dr Wangel's daughter, Bolette, she was reviewed in "The Independent" as giving a "lively identity" to the role. The British Theatre Guide described her performance as "very good". A review in "The Telegraph" said she "brim[s] with forceful vitality".


title: Sara Vickers

text: In 2011 she was Maia in "Judgement Day", based on Ibsen’s last work "When We Dead Awaken", directed James Dacre at the Print Room, Notting Hill Gate, her performance described as "brimming with intelligence and frustrated sexuality". The "Evening Standard" called her "the lively Sara Vickers". "The Guardian"'s Michael Billington gave the production four stars, saying that Vickers "lends Rubek's young wife the spirit of a caged animal".


title: Sara Vickers

text: In November and December 2011 she played Annabella in "'Tis Pity She's a Whore" at the West Yorkshire Playhouse. Alfred Hickling in "The Guardian", giving the production three stars, wrote that Vickers "makes a plaintive case for Annabella". For her performance she received a Commendation at the Ian Charleson Awards.


title: Sara Vickers

text: In September and October 2013, she appeared as Alexandra McArthur in "Dark Road", co-written by Ian Rankin, at the Royal Lyceum in Edinburgh. "The Independent" called her "a strong Sara Vickers", and "The Scotsman", "a fine Sara Vickers".


title: Sara Vickers

text: In 2014 she was Juliet in "Romeo and Juliet", directed by Walter Meierjohann, at Victoria Baths, Manchester. Her performance was described as "defiant and energetic, really showing off the youthfulness of Juliet". The "Manchester Evening News" said she was "occasionally transporting".


title: Sara Vickers

text: Since 2013, she has played the recurring character of Joan Thursday in the Mammoth Screen-produced British television detective drama series "Endeavour" for ITV, appeared through the 2019 series six, and returned in the 2021 series eight. In 2013 she was Connie Charles in the five episode BBC One drama series "Privates".


title: Sara Vickers

text: In 2015, she had a supporting role in "Waterloo's Warriors", directed by Ruán Magan, a docudrama produced by Caledonia Television for the BBC. That same year she was the character Lottie in episode one, "Perfect Woman", of series two of "Man Down" for Channel 4.


title: Sara Vickers

text: In 2016, she played Cara in one episode of the British sitcom comedy "Lovesick", produced by Clerkenwell Films and broadcast on Netflix. She appeared as Leanne Randall in 2016 in the third series of the BBC One crime drama "Shetland". In the Netflix historical drama series "The Crown", directed by Benjamin Caron, she performed in one 2016 episode as Crawfie.


title: Sara Vickers

text: In 2018, she appeared as Jane Gooding in one episode of "The Alienist", directed by Jakob Verbruggen, for TNT-Netflix.


title: Sara Vickers

text: Beginning with the premiere on 20 October 2019, Vickers appeared as Ms. Crookshanks, a main character in HBO's "Watchmen" television series continuation of the 1987 DC Comics limited series of the same name.


title: Sara Vickers

text: Vickers married British actor and RADA classmate Kerr Logan in August 2017. They have a child together.


title: Holy water

text: Holy water is water that has been blessed by a member of the clergy or a religious figure, or derived from a well or spring considered holy. The use for cleansing prior to a baptism and spiritual cleansing is common in several religions, from Christianity to Sikhism. The use of holy water as a sacramental for protection against evil is common among Lutherans, Anglicans, Roman Catholics, and Eastern Christians.


title: Holy water

text: In Catholicism, Lutheranism, Anglicanism, Eastern Orthodoxy, Oriental Orthodoxy and some other churches, holy water is water that has been sanctified by a priest for the purpose of baptism, for the blessing of persons, places, and objects, or as a means of repelling evil.


title: Holy water

text: The Apostolic Constitutions, whose texts date to about the year 400 AD, attribute the precept of using holy water to the Apostle Matthew. It is plausible that the earliest Christians may have used water for expiatory and purificatory purposes in a way analogous to its employment in Jewish Law ("And he shall take holy water in an earthen vessel, and he shall cast a little earth of the pavement of the tabernacle into it", Numbers 5:17). Yet in many cases, the water used for the sacrament of Baptism was flowing water, sea- or river-water, which — in the view of the Catholic Church — could not receive the same blessing as that water contained in the baptisteries. However, Eastern Orthodox Christians do perform the same blessing, whether in a baptistery or for an outdoor body of water.


title: Holy water

text: Sprinkling with holy water is used as a sacramental that recalls baptism. In the West the blessing of the water is traditionally accompanied by exorcism and by the addition of exorcized and blessed salt.


title: Holy water

text: Holy water is kept in the holy water font, which is typically located at the entrance to the church (or sometimes in a separate room or building called a baptistery). Smaller vessels, called stoups, are usually placed at the entrances of the church, to enable people to bless themselves with it on entering.


title: Holy water

text: In the Middle Ages Christians esteemed the power of holy water so highly that in some places fonts had locked covers to prevent the theft of holy water for unauthorized magic practices. The Constitutions of Archbishop Edmund Rich (1236) prescribe that: "Fonts are to be kept under lock and key, because of witchcraft ("sortilege"). Similarly the chrism and sacred oil are kept locked up."


title: Holy water

text: In Catholicism, holy water, as well as water used during the washing of the priest's hands at Mass, is not allowed to be disposed of in regular plumbing. Roman Catholic churches will usually have a special basin (a ) that leads directly into the ground for the purpose of proper disposal. A hinged lid is kept over the holy water basin to distinguish it from a regular sink basin, which is often just beside it. Items that contained holy water are separated, drained of the holy water, and then washed in a regular manner in the adjacent sink.


title: Holy water

text: Holy water fonts have been identified as a potential source of bacterial and viral infection. In the late-19th century, bacteriologists found staphylococci, streptococci, coli bacilli, Loeffler's bacillus, and other bacteria in samples of holy water taken from a church in Sassari, Italy. In a study performed in 1995, 13 samples were taken when a burn patient acquired a bacterial infection after exposure to holy water. The samples in that study were shown to have a "wide range of bacterial species", some of which could cause infection in humans. During the swine-flu epidemic of 2009, Bishop John Steinbock of Fresno, California, recommended that "holy water should not be in the fonts" for fear of spreading infections. Also in response to the swine flu, an automatic, motion-detecting holy-water dispenser was invented and installed in an Italian church in 2009. In 2020, because of the COVID-19 pandemic, Episcopal Conferences directed that holy water be removed from the fonts or stoups.


title: Holy water

text: A blessing, as a prayer, is a sacramental. By blessing water, Catholic priests praise God and ask him for his grace. As a reminder of baptism, Catholic Christians dip their fingers in holy water and make the sign of the cross when entering a church.


title: Holy water

text: Fr. John F. Sullivan, writing in the early twentieth century, noted that, "Besides the pouring of baptismal water ... the sprinkling with holy water is a part of the ceremonies of Matrimony, of Extreme Unction and of the administration of the Holy Eucharist to the sick, and it is employed also in services for the dead."


title: Holy water

text: The Sunday liturgy may begin with the Rite of Blessing and Sprinkling Holy Water, in which holy water is sprinkled upon the congregation; this is called "aspersion" (from the Latin, , "to sprinkle"). This ceremony dates back to the 9th century. An "aspergill" or aspergillum is a brush or branch used to sprinkle the water. An is the vessel which holds the holy water and into which the aspergillum is dipped, though elaborate Ottonian examples are known as . Blessed salt may be added to the water where it is customary to do so.


title: Holy water

text: This use of holy water and making a sign of the cross when entering a church reflects a renewal of baptism, a cleansing of venial sin, as well as providing protection against evil. It is sometimes accompanied by the following prayer:


title: Holy water

text: Some Catholics believe that water from specific shrines (such as Lourdes) can bring healing - although that water is not the same as typical holy water found in parishes, since it has not been blessed by a priest.


title: Holy water

text: A priest may choose from three other formulae found in the "Book of Blessings" for blessing water. They are to be accompanied by the priest blessing the water with the sign of the cross. They are as follows:


title: Holy water

text: V. Blessed are you, Lord, all-powerful God, who in Christ, the living water of salvation, blessed and transformed us. Grant that when we are sprinkled with this water or make use of it, we will be refreshed inwardly by the power of the Holy Spirit and continue to walk in the new life we received at Baptism. We ask this though Christ our Lord. R. Amen.


title: Holy water

text: V. Lord, holy Father, look with kindness on your children redeemed by your Son and born to a new life by water and the Holy Spirit. Grant that those who are sprinkled with this water may be renewed in body and spirit and may make a pure offering of their service to you. We ask this through Christ our Lord. R. Amen.


title: Holy water

text: V. O God, the Creator of all things, by water and the Holy Spirit you have given the universe its beauty and fashioned us in your own image. R. Bless and purify your Church. V. O Christ the Lord, from your pierced side you gave us your sacraments as fountains of salvation. R. Bless and purify your Church. V. Priest: O Holy Spirit, giver of life, from the baptismal font of the Church you have formed us into a new creation in the waters of rebirth. R. Bless and purify your Church.


title: Holy water

text: In his book "The Externals of the Catholic Church", originally published in 1917, Fr. John F. Sullivan writes: "The prayers said over the water are addressed to the Father, the Son, and the Holy Ghost, that through the power of the Blessed Trinity the spirits of evil may be utterly expelled from this world and lose all influence over mankind. Then God is besought to bless the water, that it may be effective in driving out devils and in curing diseases; that wherever it is sprinkled there may be freedom from pestilence and from the snares of Satan."


title: Holy water

text: Catholic saints have written about the power of holy water as a force that repels evil. Saint Teresa of Avila (1515-1582), a Doctor of the Church who reported visions of Jesus and Mary, believed fervently in the power of holy water and stated that she used it with success to repel evil and temptations. She wrote:


title: Holy water

text: The 20th-century nun and mystic Saint Faustina in her diary (paragraph 601) said she once sprinkled a dying sister with holy water to drive away demons. Although this was wrong to do, since it was the priest's duty, she remarked, "holy water is indeed of great help to the dying".


title: Holy water

text: In "Holy Water and Its Significance for Catholics," Cistercian priest Henry Theiler states that in addition to being a strong force in repelling evil, holy water has the twofold benefit of providing grace for both body and soul.


title: Holy water

text: The new excludes the exorcism prayer on the water. Exorcized and blessed salt has traditionally been added to the holy Water as well. Priests can continue to use the older form if they wish as confirmed by Pope Benedict XVI in , which states "What earlier generations held as sacred, remains sacred and great for us too".


title: Holy water

text: Among the Eastern Orthodox and the Byzantine Rite Catholics, holy water is used frequently in rites of blessing and exorcism, and the water for baptism is always sanctified with a special blessing.


title: Holy water

text: There are two rites for blessing holy water: the "Great Blessing of Waters", which is held on the Feast of Theophany and at baptisms, and the "Lesser Blessing of Waters" which is conducted according to need and local custom during the rest of the year, certain feast days calling for the Lesser Blessing of Waters as part of their liturgical observance. Both forms are based upon the Rite of Baptism. After the blessing of holy water the faithful are sprinkled with it and each drinks some of it.


title: Holy water

text: Holy water is drunk by the faithful after it is blessed and it is a common custom for the pious to drink holy water every morning. In the monasteries of Mount Athos holy water is always drunk in conjunction with consuming antidoron. Eastern Orthodox do not typically bless themselves with holy water upon entering a church as Western Catholics do, but a quantity of holy water is often kept in a font placed in the narthex (entrance) of the church, available for anyone who would like to partake of it or to take some of it home.


title: Holy water

text: After the annual Great Blessing of Waters at Theophany (also known as Epiphany), the priest goes to the homes of the faithful within his parish and, in predominantly Orthodox lands, to the buildings throughout town, and blesses them with holy water.


title: Holy water

text: When blessing objects such as the palms on Palm Sunday, Paschal eggs and other foods for Easter, candles, or liturgical instruments and sacred vessels (icons and crosses are not blessed, however, as they are considered intrinsically holy and redeemed), the blessing is completed by a triple sprinkling with holy water using the words, "This ("name of item") is blessed by the sprinkling of this holy water, in the name of the Father, and of the Son, and of the Holy Spirit."


title: Holy water

text: Throughout the centuries, members of the Orthodox Church have believed many springs of water to be miraculous. Some still flow, such as the one at Pochaev Lavra in Ukraine, and the Life-Giving Spring of the Theotokos in Constantinople (commemorated on Bright Friday).