See in the last lecture we had discussed the properties of unitary operators on a finite dimensional inner product space. In today's lecture I will discuss the normal operator the case of normal operators and prove what is called as the spectral theorem for normal operators on a finite dimensional inner product space. We must compare this spectral theorem for a normal operator with the one that I proved a couple of lectures ago for the silver joint operator okay. We will make this comparison just before the statement or perhaps after the statement of the spectral theorem for a normal operator. Let us look at some properties that we will require for a normal operator. So first of all what is a normal operator? Let me we have seen this before let me quickly recall the definition and prove some properties of normal operators. So definition let V be an inner product space a finite dimensional inner product space. Let T be a linear operator on V be a normal operator I am sorry I want to define a normal operator. So let me say I want to define a normal operator an operator T element of L V is called normal if it is called normal if T T star equals T star T, T star at the adjoint operator of T okay that is the definition we have seen this before let us look at a couple of examples one for the real inner product space and another one for the complex inner product space. Just a couple of examples we will define the linear transformations through matrices. So the first one let us take A actually A theta to be the rotation operator we have come across this operator before. So I am writing down the matrix first and then I will define the operator through this matrix A theta is cos theta sin theta minus sin theta cos theta for theta lying in 0 to pi define a linear transformation I will call it T theta from R 2 to R 2 by the formula that T theta of X is equals A theta X X in R 2 for a fixed theta then you can verify that T theta is a normal operator that is see this is a real inner product space so instead of star we consider the transpose T. So this equation T T star equal to T star T in this case is T T transpose equals T transpose T that is T is a normal operator okay so this is an example of a normal operator on a real inner product space. Let me give an example for a complex inner product space example 2 again I take a matrix and then define the linear transformation through the matrix say 1 I and 1 define let us call it S perhaps S from C 2 to C 2 by S of X equals A X X belongs to C then I leave it as an exercise for you to verify that S is normal that is S S star equals S star S if I remember right it turns out to be identity so these are this is a unitary operator this is an orthogonal operator okay so these are some of the examples of normal operators. Let us now look at some properties a couple of properties really for a normal operator that will be required in the rest of the discussion so the first property is the following this first property that I am going to write down should remind you of a result for a self joint operator okay so the first one is let me call it as a theorem let T be a normal operator on a finite dimensional inner product space we do not really need the space to be finite dimensional but still I will assume that V is finite dimensional let X be an eigenvector of T corresponding to the eigenvalue corresponding to the eigenvalue lambda of T then we will show that X is an eigenvector and X is an eigenvector of T star corresponding to the eigenvalue lambda bar corresponding to the eigenvalue lambda bar we will require this result in a later discussion okay so let us prove this result as I told you you must make a comparison of this result with the case of a self-adjoint operators in the case of self-adjoint operators we have shown that the eigenvalues of a self-adjoint operator are real numbers we have also shown that eigenvectors corresponding to distinct eigenvalues of a self-adjoint operator are orthogonal okay let me include the second part also eigenvectors so we have a so all the time saying is that we have a similar result for a normal operator also.  Let us show the second part second part is to show that eigenvectors corresponding to distinct eigenvalues of a normal matrix are orthogonal again this part of the proof should remind you of what we did for the case of a self adjoint operator so let me go through this quickly. The second part let T x equals lambda x and T y equals mu y where I know that mu and lambda are distinct I must show that x is orthogonal to y so I must show that inner product x y is 0 so let us start with consider lambda times inner product x y I can bring this lambda to the first argument lambda x comma y and then substitute lambda x equal to T x this is T x comma y apply the definition of the adjoint that is x T star y now use the previous result y is an eigenvalue sorry y is an eigenvector corresponding to the eigenvalue mu of the operator T then we have seen that it must follow that y is an eigenvector corresponding to the eigenvalue mu bar for the operator T star that is T star y equals mu bar y T star y equals mu bar y so this is the using the first part and mu bar is in the second argument it comes out with the conjugate and so conjugate double conjugate gives me mu times x y now the result follows if lambda is not equal to mu then inner product x y must be 0 and so x and y are orthogonal okay so x is perpendicular to y that is what we wanted to show. Let us go back and see every unitary operator is a normal operator okay but a unitary operator the entries at least when you treat the columns or rows of a unitary operator they are very much tractable in the following sense if u is a unitary operator then without writing on the board let me just explain this if u is a unitary operator then it satisfies u u star equals u star u equals identity okay what this means is the following just let us look at the equation u u star equal to identity it means that if you look at the inner product of the first row of u into the inner product of the first column of u star okay that is the inner product of the first row of u with itself then by looking at the right hand side it follows that this is equal to 1 whereas the inner product of the first row with the inner product of the second column of u star third column of u star etc the last column of u star these inner products are all 0 this is the same as saying that the inner product of the first row with the second row the third row etc with the nth row that inner product is 0 is that clear so every row of the matrix u if u is unitary has the property that every row if you take the dot product of the row with itself then it is a vector of norm 1 whereas the dot product of the vector with every other row is 0 this means what the rows of a unitary matrix form an orthonormal basis for Cn a similar argument can be given by looking at u star u equal to identity to make the following statement that the columns of a unitary matrix form an orthonormal basis for Cn a similar statement can be given for the case of an orthogonal matrix that is a real unitary operator so for an orthogonal matrix the rows and columns form an orthonormal basis for Rn for instance but the case of a normal operator is much more general the product is not equal to identity not it not so it need not be invertible a normal operator need not be invertible so the a statement about the entries of a normal operator is not easy to make but we will look at a particular case that is the essence of the next theorem that is if you know that an operator a normal operator t has the property that the matrix of t relative to a particular orthonormal basis is triangular that is either upper triangular or lower triangular then we can say something it follows there is a matrix must be a diagonal matrix okay so this is what we will show so let me make this statement precise so this is what I want to prove I will state this as a theorem let t belong to Lb where v is a finite dimensional inner product space suppose that there exists an orthonormal basis I will call it script b as before orthonormal basis b of v such that the matrix of t relative to this basis equals a is let us say upper triangular till now I have not made any assumption on t, t is just any operator with the property that there exists an orthonormal basis with a extra property that the matrix of t relative to the orthonormal basis is upper triangular or lower triangular it does not matter then t is then we can characterize normality of t necessary sufficient condition for t to be normal is that a is diagonal okay then t is normal if and only if a is diagonal as I told you this say something less about the matrix a that is you need to make some assumption on the matrix of t relative to orthonormal basis but nevertheless this will be useful for us in proving the spectral theorem for a normal operator okay okay let us see the proof of this so proof let us perhaps prove the easy part here suppose that a is diagonal by the way all the spaces are complex spaces suppose that a is diagonal then any two diagonal operators matrix is commute so I can say this much that a a star equals a star a this is always true any two see way is diagonal a star is also diagonal so this happens this means what thus what is a a is the matrix of t relative to b and a star is the matrix of a star is a star is a conjugate of the matrix of t relative to b but then we know we have proved this before that t b star is t star b so I have this equation and on the right hand side I will write a star a that is t star b into the matrix of t relative to b have this equation and there is a property that we have proved for the product you can replace that by the composition composition I will not use the circles I will simply say that t t star relative to b is t star t relative to b now this is a calculation that we have done a number of times before what follows from this is that the operators must be the same that is action of the operators so I have two operators let us say s and t the action of s on a basis is equal to the action of a t on that basis then we have seen that this defines as uniquely so from this it follows that t t star equals t star t so is it clear so t is normal if a is diagonal then we have shown that t is normal let us prove the converse part that is not straight forward the converse part is to show the converse part is to show that if t is normal then a is diagonal we will do we will consider one column of the matrix a at a time and show that all elements except the principal diagonal element must be 0 okay. So let t be normal what is given I am just reiterating and I am calling that as a matrix a right what is given is the following a equal to the matrix of t relative to b is upper triangular so let me write the matrix the form of the matrix it is upper triangular so it is something like this a 1 1 a 1 2 etc a 1 n this entry must be 0 a 2 2 a 2 3 etc a 2 n this entry must be 0 this must be 0 etc let me write the last row 0 etc 0 this is a n n. So, this is a form of the matrix a if t is normal I must now show that all these entries are also 0 this is the principal diagonal this is the principal diagonal I must we must show that all these entries are 0 okay so we will do it one row at a time okay now let us look at the relationship between the entries of a and the matrix of t relative to b in other words I will just use the formula for this equation so this says t of u j equals summation i equals 1 to n a i j u i this is true for all j 1 less than or equal to j less than or equal to n.    Now a 11 bar u 1 that can be cancelled look at what remains what remains is a 12 bar u 2 etcetera plus a 1 bar u 1 equal to 0 now u 1 u 2 etcetera u n form an orthonormal basis in particular they are linearly independent so subset is also linearly independent so u 2 etcetera u n is linearly independent subset so this is an equation like let us say alpha to u 2 etcetera plus alpha n u n equal to 0 so each of the scalars must be 0 so what follows is that a 12 bar so see the conjugates are 0 so the complex number also must be 0 so a 12 equals a 13 etcetera equals a 1 n all these must be 0. These are precisely the first row entries except the first entry so the first row entries have been shown to be 0 what we have shown is that a 12 a 13 etcetera a 1 n they are all 0 in particular okay in particular see we will appeal to induction but we need to make one observation in particular a 12 is 0 so if you look at the formula for t u j when j equals to what happens the formula for t u j when j equals to gives me a 22 u 2 and that is like this equation I am sorry yeah that is like this equation t u 1 equals a 11 u 1 so once I have a guarantee for that then we can appeal to induction that is I will say that in particular what follows is that t u 2 equals a 22 u 2 because a 12 is 0 and so I am looking at the second column all entries below a 22 are already 0 because it is an upper triangular matrix now what follows is that u 2 is an eigenvector corresponding to the eigenvalue a 22 for the operator t so u 22 will be an eigenvector corresponding to the eigenvalue a 22 bar for the operator t star I proceed as before there are only finitely many columns so it follows that a is diagonal okay so I will simply say by induction it follows that a is diagonal okay now this is an important intermediate result in order for us to prove the spectral theorem for a normal operator okay now before going to the spectral theorem we will prove what is called as a Schur triangularization theorem okay Schur triangularization theorem so let me write this theorem this is called the Schur triangularization theorem Schur triangularization the statement is a following let V be a finite dimensional complex in a product space and t be any operator now this result is true for any operator there are no conditions on t normality there is no such condition so what is the statement finite dimensional complex in a product space t is a linear operator on V then it says that you can do a little less than diagonalization then there exists an orthonormal basis script V of the vector space V such that the matrix of t relative to B is upper triangular okay for any operator t on a complex inner product space what is important to observe is that the Eigen values belong to the underlying field because C is an algebraically closed field okay so let us understand that there is no counterpart of this result for the case of a real inner product space however if you know that t is an operator on a real inner product space with the property that all the Eigen values of the operator t are real then we can write down a similar statement okay so let us understand the importance of the fact that this is a underlying field is a complex field it is an algebraically closed field okay we will show that is upper triangular the proof will be by induction okay proof by induction on the dimension let us call this n on the dimension let us call this n the case n equal to 1 there is nothing n equal to 1 it is trivial that is when n equal to 1 what it means is that we want to show that there is an orthonormal basis such that tp is upper triangular there is just one entry so 1 cross 1 matrix now what is that matrix so this is where we are using the fact this is a complex inner product space there is an Eigen value for the operator t there is an Eigen value for the operator t in other words in other words let me say that there exists x not equal to 0 such that such that tx equals lambda x for some complex number lambda we can call the x1 as x by norm x the Euclidean norm x is well defined then it follows that tx1 equals lambda x1 with norm x1 being 1 you take the basis consisting of that just the single vector then the matrix of t relative to b is the number lambda which is trivially upper triangular let us assume that the result is true for finite dimensional inner product spaces of dimension n minus 1 and then prove it for spaces of dimension n so in that the induction hypothesis is made we will prove this result for all finite dimensional inner product spaces of dimension n so let us take dimension of v to be n let us now start with okay suppose dimension v is n see we made a statement that the operator t has an Eigen value a similar statement holds because the underlying field is complex a similar statement can be made for t star so let me exploit that let x not equal to 0 be such that this time t star x equals lambda x for some complex number lambda existence of an Eigen value so there is a by definition in on 0 vector x satisfying this equation let us now define w to be span of this vector x and take its perpendicular so w is span x perpendicular then what follows is that then observe that x belongs to w perpendicular okay x belongs to w perpendicular so what it means is that t star of w perpendicular is contained in w perpendicular that the space w perpendicular is invariant under t star because x is an Eigen vector okay so one dimensional w perpendicular is a one dimensional subspace span by the single vector x okay now t star w perpendicular is contained w perpendicular we know that this is the same as saying that t of w is contained in w this is one of the results that we proved earlier if t star is if w perpendicular is invariant under t star then w perpendicular perpendicular must be invariant under t star that is w is invariant under t so t w contained in so it makes sense to so s from w to w defined by so I define a new operator s this is defined as the restriction of s to the restriction of s I am sorry the restriction of t to w this is well defined so this operator is well defined s from w to w is well defined see all that I need to know is that if you take an element w and w whether s of w belongs to w okay but by the definition s of w is t of that little w but t of w is contained in w so this s is well defined this is another construction that we have used when we discussed the self adjoint operator case so s is well defined what is the dimension of w what is the dimension of w dimension of w is n minus 1 see it is orthogonal complement of a single vector so dimension w is n minus 1 I have an operator s I have an operator s on a finite dimensional neoproduct space of dimension n minus 1 so the induction hypothesis is applicable that is there exists an orthonormal basis so let me say there exists an orthonormal basis let me write down the elements as u1 u2 etc may be x1 x2 etc x n minus 1 right this space is of dimension n minus 1 orthonormal basis of w such that such that the matrix such that the matrix of s relative to this x1 etc xn minus 1 is upper triangular okay so I have this by the induction hypothesis let us just write this in full and see what it says okay but before that let us I will make use of this and then define a new vector xn as the first vector x that we started with divided by its norm the vector x that we started with the norm of norm 1 so I will take that divided by its norm and call it xn then it is clear by the construction that the vector x1 x2 etc xn minus 1 which have been obtained before and the vector xn that we have defined newly through this vector x is an orthonormal basis. This is an orthonormal basis for v that is we are writing v as w plus w perpendicular and then for w this is a basis orthonormal basis for w perpendicular x2 etc xn minus 1 is an orthonormal basis so come we know that when you combine these two it gives rise to orthonormal basis for v all that we need to do is to look at the matrix of t relative to this basis script b which means what you need to look you take t apply it on x1 write it as a linear combination of x1 etc xn minus 1 xn etc finally take xn look at the image of t look at the image of xn under t write it as a linear combination of x1 etc xn now t x1 x2 etc xn minus 1 belong to w and the action of t is like the action of s and for s I have an orthonormal basis I am sorry the form of the matrix of s relative to x1 etc xn minus 1 is upper triangular okay so let us make use of that. So all that I am saying is that the matrix of t relative to this basis b is of the form let us say a11 it is upper triangular for the first a12 etc a1 n minus 1 then it is upper triangular this entry is 0 a2 to etc a2 n minus 1 etc all these entries are 0 a n a n minus 1 n minus 1 and then look at what happens so this purely comes from the matrix of s relative to x1 etc xn minus 1 what is t of xn t of xn see xn belongs to w I am sorry xn belongs to w perpendicular and so I have I make use of this invariance of space thing so what follows is that the last entry will be 0 0 etc lambda okay just check these steps now it is now clear that this is a required form and so the matrix so if t is normal I am sorry if t is an operator on a finite dimensional complex in a product space then the matrix of t relative to b is upper triangular this is the so called true triangularization theorem let us now move on to prove the spectral theorem for a normal operator spectral theorem for a normal operator let t be a normal operator on a finite dimensional complex in a product space v then there exists a basis script b of v such that the matrix of t relative to b is diagonal that is every diagonal you can say this is the same as saying that this is a matrix version of the statement that if you have a complex normal matrix on if you have a complex normal matrix then it can be diagonalized by a unitary matrix there is also another way of stating this which is that if t is a normal operator on a complex finite dimensional in a product space v then there is a basis orthonormal basis b of v which has a property that each vector in the basis is an eigenvector for t we have seen this before we have seen the statement before so let me not emphasize okay how does the proof go it makes you suffer the previous two results the true triangularization theorem and the fact that if the matrix of a linear transformation corresponding to an orthonormal basis is triangular then the operator is normal if and only if the matrix is diagonal okay so let me say by Schur's theorem Schur's theorem is applicable for any operator by Schur's theorem the matrix of I will simply say there exists a basis such that such that the matrix of t relative to b let us call it as a is upper triangle this upper triangle so that is Schur's theorem now a is upper triangular appeal to one of the results the earlier result that we proved since t is normal it follows that a is diagonal which is what we wanted to show that is there exists an orthonormal basis b of the vector finite dimensional vector space in a product space v with the property that the matrix of t relative to this basis is a diagonal matrix okay now you must compare this statement with the statement for a self adjoint operator see I will leave it as an exercise for you to write down the matrix versions the matrix version is something that I told you immediately after writing down this theorem so that is anyway there now you must compare this with the spectral theorem for a self adjoint operator where the underlying inner product space was not assumed to be complex okay to summarize this is what we have if you have a self adjoint operator on a finite dimensional inner product space it does not matter whether it is a real inner product space or a complex inner product space it always has the property that there is an orthonormal basis for the space v which has the which also satisfies additional condition that each vector of the orthonormal basis is a eigenvector for the operator t for the case of complex for the case of normal operators I have already made this I have already made this statement that if you have a normal if you have a normal operator on a real space then it is not necessarily diagonalizable that is if t satisfies t into t transpose equal to t transpose into t then it does not necessarily follow that t is diagonalizable the example that was given was that of the rotation operator which we also see which we have also seen in the beginning of today's lecture but if it is a complex inner product space and t is a normal operator then there is an orthonormal basis with the property that each vector is an eigenvector let me stop.


Hi everyone, Joe for JaspysCaseBreaks.com with 2020 Top Synception Baseball 1-Bot Random Team No. 7 and a chance to win two transcendent spots in this, which should be pretty awesome. There's only a 29 spotter as well, so your odds are slightly better than some of the other mini-breaks that we have to get into the transcendent. No cardinals in this, which is why it's only 29 spots. Let's roll and randomize it one and three, four times for each list, one, two, three, and four. So this is just for the break, obviously. Stephen K, down to Derek E, four times for the teams, and fourth and final time. After four we've got the Los Amai Dodgers, down to the fish, Miami Marlins. Now I'm not going to read off all these names for this, just for this little one-box break, but I will just show you. I think most people just want to see who wins the spots anyway. Stephen K got my Dodgers. Derek last bot Mojo with the Braves, that's the last bot Mojo star next to his name. All right, now let's alphabetize it by team. Any trades? Just one auto, sometimes you get a bonus, but just one auto per break, per box, that is. There's the box right there. Everything ships though, of course, in this one-box inception. No, no trades. All right, let's close it up. Matt Gomes counting on me to win a spot. Don't count on me, Matt. You've got to bribe random.org. You've got to bribe them. I'm just the guy that presses the buttons. You've got to whine and dine random.org. Can't count on me. I have nothing to do with it. I have no influence on who wins spots or not. Zero influence. All right, there it is. At Jaspy's Breaks, Dennis is our Twitter handle and our Instagram handle. All right, let's lead off with Aaron Judge to 75. There's Jack Flaherty and the rest. And behind Jordan Yamamoto is a patch auto and it's going to be Will Smith, the fresh prince of Bel Air. Stephen Kay with my Dodgers. The Dodgers future backstop. I guess you're starting catcher with Austin Barnes behind him. Nice, pretty solid player. All right, there you go. Nice little Dodger, Joe Mojo. Now let's see who wins spots. Two spots to be precise. Top two spots are going to be intranscended. So good luck. New dice roll for this, just like it's break credit. Three and a one, four times. One, two, three, and a one, fourth and final time. Thanks everyone for giving this shot and congrats to Tim and Jared. Both of you have $450 spots. That's the value of it. Transcended Baseball Hall of Fame Edition. It's going to be great. Drops on Friday. Check it out on jaspyscasebreaks.com. Thanks for watching, everybody. See you next time.


We have witnessed a significant assault on the fundamental freedom in this year alone, but also in the past year, especially in this 2020 during the COVID time as well. We have documented over 120 individuals have been arrested because they have exercised their fundamental freedom. In the last few months since July, the government has arrested a number of activists and mainly they are the young activists. They are environmental activists.  So, you know, like most of the youth come to the street to demand the release and then they have been arrested. Now they are in detention. And today I saw the tweet by the special reporter on the Human Rights Defender Mary. They have tweeted about the case because the family of those young have sent the message with the photo of their children.  And, you know, few are the young, they are the rap singer, they also accused because their song are critical against the government.


Bemidji State University wants to make sure our veterans feel appreciated. Lakeland News reporter Cheryl Moore has a preview of their tribute that will be going on for this week's Community Spotlight. Veterans Day may not be until Sunday, but BSU is celebrating all week long. We have over a hundred students that we that we know who are who are identified as veterans. Today a flag-raising ceremony was held on campus as well as an open house at the BSU Veterans Assistance Center in Decker Hall. As we approach you know Veterans Day it's a way to for us to honor them and to celebrate them for the service that they have given to our institution as well as our country so I am proud and was humbled to be serving in this capacity. If you feel like bringing the elements and showing some support for our veterans BSU has activities planned all week long. Tomorrow will be an event called Voices in the Field where BSU alumni and staff who are also veterans will speak about their experience and to give us a perspective of what it's like to actually be a military person and the things they will want us to know while we are you know worried and concerned about them as they are taking time overseas during deployment. On Wednesday we're having our missing men table where it's a table where we talk about celebrating celebrating our veterans but it's a part of our missing man piece of those people who have served in Vietnam and who are prisoners of war and on third stage we're showing the movie above Sunrise which tells the story of two service men who took a journey from Wisconsin to California to bring awareness to mental health issues. All of this week's events will start around noon to make it convenient for staff and students although the whole community is welcome to come. If you have access our activities are on our on the university website if there's questions please are free to call the Dean of Students office and that number is<PHONE_NUMBER> and we'll be happy to give you that information. Officials at BSU tell me events like these have been going on at the university for a number of years. In the future they plan to continue the tradition. With this week's community spotlight in Bemidji, Sheryl Moore, Lakeland News. And BSU will be closed this Friday to observe the Veterans Day holiday. If you've enjoyed this segment of Lakeland News please consider making a tax-deductible contribution to Lakeland Public


And we're just going to jump right in. Everybody ready to jump right in? OK. Thank you for coming. I would like to now introduce Emerson College's president, Leap Helton. Well, good evening, everyone. I want to welcome you to Emerson College. I'm Leap Helton, president of Emerson, and I am very, very pleased to see so many people here for what is sure to be an important conversation. Of course, I want to thank Arts Emerson and the American Repertory Theater for hosting this wonderful and thought-provoking event, which is part of the Citizen Read Project. And of course, I also want to take a moment to welcome and recognize the many members in our audience who happily participated in this project. You know, for the last several years, Emerson and Arts Emerson have enjoyed an extraordinary and really beautiful relationship with Claudia Rankin, a relationship that began in 2015 shortly after the publication of her groundbreaking book, Citizen, an American Lyric. And last year, I was honored to bestow up on Claudia an honorary doctor of humane letters from Emerson in recognition of her many achievements and contributions that underscore our own values and beliefs at the college. Here at Emerson, we are committed to excellence, to diversity and inclusion, and to global and civic engagement. These institutional priorities reflect our college's rich history and our hopes for our future. Above all, we are committed to inclusive excellence. Emerson in all that we do is shaped by the diversity of people and ideas and perspectives and beliefs and our commonwealth of learning. And Emerson education is profoundly rooted in creativity and excellence and innovation. And members of the Emerson community share an innate desire to create, to use their chosen disciplines and medium to make a difference. We are the doers, we are the makers. And here at Emerson, we believe in the infinite value of the arts. The arts connect diverse people and ideas and disciplines and shine a bright light on our shared human experiences. The arts help us to comprehend in new and wonderful ways the world in which we live. And it helps to prompt important conversations about our shared and common humanity. Tonight, Arts Emerson and ART provide an important platform, a commons, to make those connections to re-examine ourselves and confront our beliefs. And most important to open our minds and hearts to diverse cultures and perspectives that surround us. And at this particular moment in our country's history, I'm sure you'll agree with me that it seems more fitting and more important than ever to use the arts, to lift up the arts, and to use the arts as a platform to move these important conversations forward. And to begin, I invite you to enjoy this short video which was created by Claudia Rankin and John Lucas. And now, situation seven. Thank you so much. On the train, the woman standing makes you understand there are no seats available. And in fact, there is one. Is the woman getting off at the next stop? No. She would rather stand all the way to Union Station. The space next to the man is a pause in a conversation you are suddenly rushing to fill. You step quickly over the woman's fear, a fear she shares. You let her have it.   He has had to think about it so much, you wouldn't call it thought. When another passenger leaves his seat and the standing woman sits, you glance over at the man. He is gazing out the window into what looks like darkness. You sit next to the man on the train, bus, in the plane, waiting room, anywhere he would be forsaken. You put your body there in proximity to adjacent to alongside within. You don't speak unless you're spoken to. And your body speaks to the space you fill and you keep trying to fill it, except the space belongs to the body of the man next to you, not to you. Where he goes, the space follows him. If the man left his seat before Union Station, you would simply be a person in a seat on the train. You would cease to struggle against the unoccupied seat when, where, why the space won't lose its meaning. You imagine if the man spoke to you, he would say, it's okay, I'm okay. You don't need to sit here. You don't need to sit and you sit and look past him into the darkness. The train is moving through a tunnel. All the while the darkness allows you to look at him. Does he feel you looking at him? You suspect so. What does suspicion mean? What does suspicion do? The soft gray green of your cotton coat touches the sleeve of him. You are shoulder to shoulder, though standing you could feel shadowed. You sit to repair whom? Whom? You erase that thought. And it might be too late for that. It might forever be too late or too early. The train moves too fast for your eyes to adjust to anything beyond the man. The window, the tile tunnel, its slit darkness. Occasionally a white light flickers by like a displace sound. From across the aisle tracks room harbor world a woman asks a man in the rose ahead if he would mind switching seats. She wishes to sit with her daughter or son. You hear but you don't hear. You can't see. It's then the man next to you turns to you. And as if from inside your own head you agree that if anyone asks you to move you'll tell them we are traveling as a family.  We want to be able to see people and have people see each other just a little bit for one minute. I'm Diane Borger the producer at ART joining David for just a little preamble before we get to the main event. It's been a fantastic experience for us to partner with ArtsEmerson on both the production of the white card and also the civic engagement activities around it. So I'm formally thanking him. Well and thank you so much for the partnership Diane and ART. We're both delighted, both organizations are delighted to have sponsored this total event the Citizen Read and that you participated. I just want to let people know for those of you who aren't aware of what even the Citizen Read has been and there may be some of you in the audience and certainly maybe some of you at HowlRound. I see you guys over there streaming this event. Thank you. So Citizen Read has taken place all across the city. We've had 1,300 people participate in 80 different book clubs and if you could just wave and say where your book club participated. The book club leaders in the audience just shout it out. Where were you? How were you from? You hear that? All over the region and thank you so much for participating and then we also have in the house today a number of the facilitators so what happened was that book clubs all over the city read the book and had facilitated conversations with trained staff that was provided by ART and ArtsEmerson to have the conversations. I think there are about 20 of you in the house today who were facilitators of those conversations. Do you want to wave? They're all sitting over there together. This is also the facilitation team at the white card. For those of you who are seeing the play you might recognize a few of these facilitators for the act two conversations. Thank you for your work. It's been an incredible journey with you and we so appreciate all of your time and effort and your expertise in this conversation. There are a couple other little thank yous to do. We, oops I'm on page two already. For those of you who haven't read it I just want to let you know it's not too late and thank you to Nicole Olossania and DeBrena from ART and Kevin from ARTSEmerson and Robert Duffley. The resource materials for the Citizen Read are available online at artsemerson.org and you can still in your book club or individually read the book and follow the curriculum. You have time. The play is here until April 1st so you can do it at any point and it will enrich the experience of watching the play and there is no way that ArtsEmerson and ART could have achieved the project on our own so I want to thank all of the teams at both of the theaters, all of the facilitators of the book clubs and all of the facilitators of the conversation for making it such a vibrant kickoff to this culminating event Citizen Speak. So it's my lucky pleasure to introduce the two people who are going to talk about it today so Claudia is obviously here and she'll be talking about the journey from Citizen, the book of poetry to the play, The White Card and she's joined by Pete Carl who's been the dramaturg on the production. Pete Carl is a distinguished artist, I want to get the titles right, and the residents at Emerson College, the dramaturg for The White Card as I said and also a recipient of the Art of Change Fellowship from the Ford Foundation. Claudia who needs no introduction is the author of five collections of poetry she's a professor at Yale but she's also with Citizen in particular won a list of prizes that takes up the whole card so I told her that I probably wouldn't read all of them but she won many of the poetry prizes the year that it was published she won the National Book Critics Circle Award for poetry she won the forward prize and she was awarded a MacArthur Genius grant but for me she's today first and foremost the playwright of The White Card so Carl and Claudia we welcome you. Good evening hello hello thank you all for coming out this evening I have had the great privilege this last two years to work with Claudia on her amazing play The White Card. How many of you have seen the play? Okay not enough. Not enough yeah yeah I know some of you are going later I know you're all going to see it but you may not have seen it yet and as we were working on the play and talking about how to engage Cambridge and Boston in the conversation of the play I asked ArtsEmerson in ART about the idea of doing a read of her book Citizen because it felt like the Citizen and The White Card and of course all of Claudia's work is in conversation with itself in a way and that there would be a wonderful trajectory of being able to read the book in community with other people then be able to talk with Claudia about the book and then also be able to read the play and then participate in the act two conversation that the play offers after the show that it could really I know you know we are a community grappling with race I don't know how many of you read the spotlight series in the Boston Globe but I did and it was not shocking but it was sobering I think and so it feels like a great time for us to be kind of digging deeper so what we're going to do tonight many of you have submitted questions from your various reads so I'm going to go through some of those questions and we're going to start really talking particularly about Citizen. Claudia you published this book in 2014 how many audiences would you say you have talked with this about this book with? Well after the election I would say not enough apparently apparently um I you know I I don't know I don't know it's been it's been a gift to be able to travel this country and and beyond our borders in order to hear what people have had to say around racial dynamics specifically in the United States so I haven't counted because it hasn't been a burden because it has informed me in ways that you know before the process I don't think I could have um felt confident to speak or to write the white card in fact uh as we've been working on the play I mean I know at least every week it seems that you travel somewhere to have a conversation and uh and it and um and really rich conversations uh I wonder if maybe um just to start what are a couple of things that stand out I mean as you've toured over really like it's about three or four years now that you've been touring talking about the book what um what are some of the responses that really stand out to you in terms of conversations that you've had? I think I think the thing that um has most surprised me is how we are living two different realities um and I mean we as in people of color because I was also surprised by the number of Asian women especially who came up to me and said this book is their book so there is sort of white America and um and then the rest of us who were being subject to a certain kind of um projection and it it was surprising to me that it was not seen as it was happening I um I thought I'm seeing it I'm feeling it and apparently other people are and yet um the book for many people was a surprise and I found that surprising um so uh I have a kind of um I have your actual legitimate questions here on no cards that you have met some of you in the audience have asked so I'm going to go through some of them and we'll just kind of chat a little bit and uh uh and then we're going to chat for um about an hour so uh the um uh one of the questions uh was um if you could talk a little bit about your emotional process writing the book were some parts more challenging to write than other parts and why? The you know as with most books you don't think you're writing the book when you start writing the uh citizen began with Katrina and um when Katrina happened many people said how could this happen and and it became sort of an irritant for me because I thought come on come on we you know we we know that this some form of this is happening all the time but when I did the Katrina piece which became a situation video I didn't really know that it was towards a book but first I responded with my husband to Katrina and then we began to respond to situations in the culture moments in media that caught our racial imagination and then I was diagnosed with breast cancer and um I was home and for you know for the first time in a long time when I said no to somebody they believed me you know like they're two times in your life when you're pregnant you can be like no I'm pregnant and people are like oh I'm sorry that's okay and the other time is uh no I have cancer and then they're like oh okay that's fine we'll find somebody else to do it you just go home and take care of yourself and so I was able to be home um you know with the chemo and the radiation and all that but I was home and I was able to sit down and really work through some of these um situations on the level of language and really without interruption every third week I had to have chemo so then I was sick and then I didn't work those weeks but the other weeks I um I was able to really kind of think about um how stories that had been told to me could be communicated in the language so it was really that trajectory from Katrina to about 2013 that I worked on the book um and then um uh I know there's a way in which the book is laid out and you and I've talked about this um about the uh maybe and you can just uh you know expound a bit about the way um you you know sort of intentionally shared each piece of the book in the way that you did and how how you were thinking about that well I wanted the book to accumulate so that we start with um um moments of microaggressions or racism or implicit bias whatever language you want to use that come and go so quickly that um people don't even remember that it happened I mean the person who is feeling it doesn't forget it but the other person who might be saying a thing or doing a thing um will have moved on so quickly and so I wanted to begin with those so that we could understand that these small aggressions actually are a kind of complicity that allows for the larger aggressions so that the fact that um abandoning an entire community of people during Katrina for example could happen it can happen only because every day these other forms of rendering people invisible were also happening and they were happening you know with colleagues and um at the grocery store in in small ways and then when it happens in larger ways we are surprised so I wanted the book to build to that so that's why the situation videos um the text for those happened later on in the book and then I thought I needed a sort of more lyrical section that addressed the internal feelings around what it feels like to be inside these moments and um so the more lyric piece ends later the piece with Serena Williams the sort of essay lyric essay piece that happened very intentionally because I wanted to create a piece that you could look up the other pieces were um stories being told to me I had called my friends and asked them to share um incidents of of racist things being said or done to them but that was still hearsay and you know when I was out of college I went to college not far I went to Williams and then I was going to go to law school and and so and I worked in a law firm for a while and I began to think you know this is just hearsay why should anybody believe this so I thought you need to write something where people can look up everything in them and so I thought about who is being subject to um to racism all the time that is documented and that can be shared in our collective imagination and I first thought about um Tiger Woods but he's crazy so I was like no he might be subject to racism but he's also crazy um so I didn't use I didn't use him but then I I remembered Serena Williams and and I thought it would be interesting to write a piece that just tracked her history at the US Open and um so that's that comes very close to the beginning of the book because I um I wanted people to I wanted people to say no this doesn't happen and then be able to go to YouTube to prove that I made it up and see that no um this people cannot help but project onto black people um ideas around criminality animal um you know if you think of everything that's been said about Serena Williams um being called brother being called um all kinds of things and so it's all there and so it wouldn't be you wouldn't be relying on me or my memory or my interpretation of the moment um so that those were the kinds of the decisions I made in in it sort of artistically inside that book just a interesting not so interesting note of um as we were making the play um and then uh right towards the end of um you know before the production Serena came up again because the um Australian Open was on which is how the play starts and um there is a white supremacist tennis player from Tennessee who had um all these things on his Facebook page and one of them was you know something derogatory about Serena so it was like it was it just keeps going just keeps going and going which was um not a fun part about making this play uh I have to say um this is a question uh it's more of a comment but I think it's a great comment that you can we can turn into a question uh somebody who says what stood out to me about this work was the way in which it used at times an accumulation of accounts of what some would perceive as microaggressions to really show the vastness and compilation of such experiences and how that accumulation wears down on one's sense of self however even as this intensity built I did not get a sense of a moment of release at least not on this first read so I'm wondering about moment of release well that was the idea that the book you know when you when you think about the work of a writer or work of an artist um it actually is very boring on a certain level because you are thinking about how do you keep questions craft questions like how do you keep the tension in this book going and so the design of the book in terms of the trajectory of the the book had to do with accumulation of experience so that it's one thing on top of another thing on top of another thing on top of another thing and then a redirect and then more one thing on top of another thing on top of another thing and then redirect and and I want for example the images in the book I spent a lot of time thinking about which images would offer conversation but not release you know so that the image would be in conversation with the tax and the eye even the placement of the images on the page had to do with so the eye can move from the tax move into a different bodily relationship to the text but not be released from the text and um so all of that the the sense of accumulated assault really was part of the design of the book um I mean down to one of the the fights I always have with my publishers whether or not my picture should be on the back cover and you know because they think of you is um I love my publisher but I think in the world of publishing they think of you as a brand and so they think if somebody sees your picture they'll buy the book but I always felt like no don't put any picture there because I don't want people to feel like this is my life I want the book to stand as a kind of experience on its own um and you know it took a long time to get them to to say okay to that but that's their and that desire was to prevent the desire of because I do it as a reader so I know so that you don't sort of flip to the back of the book and start looking at me and thinking oh I wonder um how she's doing you know and um so all of those decisions had to be decisions to maintain that line of tension and that that experience of accumulation yeah it's interesting when I've talked with people about the book and taught it sometimes people think that all of those experiences are yours and I think the the effort to separate yourself from that has had to be intentional in that way so this comes from another book club member someone mentioned in a book club that they didn't believe Claudia Rankin that would be you presented enough evidence to show that one of the instances she discussed was race-based this led me to the following questions I wish I'd asked him in response if this text was evidence what was the case what was the case being made for how much what kind of evidence would convince him at what point is there just acceptance resistance to seeing well this is the thing this is why the book is just a book you write the book from the position of this is what I know this is what I feel this is what's been told to me this is um this is a life contributed by many people if the person reading the book refuses the book that's another kind of decision and I'm not really a part of that you know um it seems to me that if someone feels the book fails in their ability to recognize another human being's um experience in life that's its own position right and and if I were that person I would then start asking myself what is it I need from this book that I'm not getting because then that's you know that's a generative um question that would allow for a re-entry into the human experience rather than the idea of the rejection of the thing as a failure um so that's I'm at least for me that's how I'm I'm I'm always interested in in what is it I wanted that I feel I'm not getting you know I was in London um at a BBC the BBC does these uh they do these talk things it's sort of like this and they do them in maybe November so that people can go on vacation for Christmas and and then they put you in a room with people and somebody talks to you and there's a Q&A and but it's a real Q&A not like this one where it's managed and you can't really speak which is good but there was a guy in this Q&A and he said to me you know I read Citizen and I like Citizen but um but I don't I don't really find you that interesting and and I said to him if you would tell me what you would like for me I will consider it because it really is about a kind of performance that one wants right and if that performance is not forthcoming it's as much on your desire as it is on the thing in front of you yeah I mean I'd love to get into this just a little bit in relationship to the white card because uh you know one of the things as you and I started making the play um and we start talking and and you would write things and I would say things to you like oh that's too that's too extreme that's that's going too far and you would say oh that happened last night uh you know like and um and so you know it was it certainly for me was an education I didn't come in um uh you know ignorant to it but I I didn't come into it uh knowing the um the constancy of it especially for someone like yourself who is you know by your very presence provoking for people this question of of race but the um uh so every time you walk into a room people are bringing you know bringing it up and and and then when we started working on the white card uh and you know this is you know you'll you'll read this if you you know read about the play um you know people saying well the white characters aren't believable um and of course uh we know that they're utterly real um and that everything that's spoken in that play has been said um and so what like that question of convincing like how is it that um you know in every circumstance it is this kind of choice to distance yourself and to say those things aren't believable and to um and to really um uh kind of stand by that and I I've just found that very curious like what are real people then if these are not real people like and why can't white people believe how white people behave I find that um that's been a really curious thing uh to witness through the course of the play well yeah I you know it's such a hard um it's a hard thing because I've been thinking about that in the course of making the play I I mean you know it's anecdotal but um just a couple weeks ago I was at a dinner and um and I was flanked by these two women very nice women very nice women very very important women in our community and um but one of them said I don't understand um why white people are so racist um these are you know she said um it's probably reverse racism but I think black people are superior to white people I mean they're great athletes and singers they have a lot of rhythm I did not make that up at all I mean when people think I make this stuff up they give me too much credit yeah they really do and then the woman on my other side she said well there was a woman on across from us a white woman across from us and she started going um oh my god what is she saying oh my god what is she saying which I thought would be a really great um like chorus some backup singers oh my god what is she saying oh my god what is she saying so she's you know and the woman just kept going she's like no they're great singers great great singers some of our greatest singers are are African Americans and um so this happens and then the woman on my other side she says you know Claudia white people are very racist if I told you some of the things I thought you wouldn't believe it and I'm eating dinner between these two women you know I'm like okay this is let's go this is our evening together um I can't make this stuff up I cannot make it up I would be I would deserve something better than the MacArthur but so you know so when people say to me this is not believable I think what they're really saying is I am not in the room with black people ever and and and scene right um uh another person who is in a group it is difficult for me to even have this kind of facilitated conversation in such a white dominated group where for most people these are shocking horrific lessons and where for me this is daily life how do you navigate this kind of situation well you know the world is um full of white spaces and um I you know I can't remember a time in my life where I have not been in spaces that were dominated by white people um you know I went to Williams College I loved Williams but hello you know um I went to Columbia I had a great time there but hello um I taught in institutions where often um I was the only black faculty member I remember one job where I I said to them look you people I'm a poet you better just hire yourself an African Americanist you can't have me doubling up I that's not what I do you could hire one of those people um so that has been my life and inside that life are also just people so I have had very good friends um who are white I have had very good friends who are black or Asian or Hispanic um but in terms of institutional power we have all been aware of the fact that we're inside white spaces and that those things are being privileged and if like every every moment you're clocking these things and they're subtle I remember once going to a dinner party at the chair's house um at a university where I was teaching and when I got there the his wife said to me would you like to see the house it was a very nice house is if you think large is nice it's nice and um and I said sure and I looked around and my other colleagues thinking they would come too but nobody moved so I stood up and then I realized oh you all have been here before and even though I've taught in this department for over 10 years this is my first visit to the very nice house my first invitation so it's moments like that like it takes a second you're like aren't you coming we don't have to we know where every room of this house is so you know it's those moments you're just you you clock them it's not you know she she had good colors on the wall yeah it was nice it was nice but I just I think I think you know my husband is white my daughter is mixed race she just started a club at her school for misraised children I I think we're negotiating these spaces and these spaces are what they are and I think if we begin this is my own personal feeling if we begin to call out the problems within the space we will begin to see them because I think everybody is culpable no matter their race in allowing things to stand and that's part of why they have stood um I also know that I am in a privileged position that my job is not on the line when I'm like hey what are you doing what are you saying um I I have colleagues who say I would say something but if I said something it might affect my tenure um so I understand that it's a complicated dance inside these spaces that are dominated by white people that are um where the habits of whiteness are maintained and perpetuated and so constant that they seem normal I was you know I was once at a hiring and a student said about a candidate who was not white he said I don't you know I don't think he's a good idea because he doesn't like it's not what I'm used to he doesn't sound like the other guy who I who I feel like speaks in the way that I'm used to reminds me of myself he said that and so I said hey do you hear what you're saying you're saying because you see a reflection of yourself that's what we should hire no one else said a thing and then a few days later that student knocked on my door and he said I've come to apologize because another faculty member said uh that I made you angry I said you didn't make me angry you were just being racist there you go um you don't have to tell the story if you don't want to but I'm the story that's in my head now is the one uh about um that award that you got and the story that was told about family but if you I don't I don't want to like I that one is in my head for some reason and it's such a great uh story about I mean just this idea of how people while white spaces are controlled that way it's a it comes to my head well um Carl has been you know we're working together for two years so every time I come back from an event I'm like Carl guess what happened I know a lot of them so I don't want to reveal ones you don't want to reveal so but um but I did get an award and um and at the ceremony the the the award was endowed by a very wealthy family and the man got up and he said he said you know race has always been important to us um in our family there were four did I say four five of us there were five of us my nanny was an important person in our family and that person has um you know been like another family member so Claudia we're so happy to give you the and you know it's like is that associative what you know I feel like I should go with the shrink you know with the shrink with me and and that that scenarios happen many times when I have received award and I finally got to the point where one man said it to me not on the podium but next to me at dinner he said he said you know um I you know we we have always had black people in our family um I grew up with a woman who who took care of me like my mother so and I know I shouldn't have done it but I said to him do you know any black people you don't pay and he said what it also makes me think a little bit about um as we've been working on the white card and uh you know some some of the people who have read it uh particularly um maybe a little bit younger generation have asked um so the play for those of you haven't seen it I won't give too much away but um is about an African-American artist who goes to the home of a white philanthropist and art dealer and has a dinner um and and many people have said oh charlotte's the character's name charlotte would never uh she would have never stayed in that room with those people and um and I just wonder if you could talk a little bit about that because that was a response we didn't really see coming in a way yeah yeah we had many black people say um um I would have left this this is not realistic if I were in a room and people were talking to me like this I would have left and it was it was curious to me because I have never been in a room where any black person have you know walked out if it was a job interview or if it was something where in some way their life would be extended in some way so I think I mean it could just be me but I I found that perplexing this notion that there is an alternate reality where you are able to negotiate a life without negotiating whiteness and racism and that one can just walk out when um when these things happen as if we don't have 401ks as if we don't have mortgages as if we don't have health insurance attached to these institutions so I mean I I I I I like to think of myself as standing up for myself but I also know I have a child at home you know I I want to have a roof over my head so as a person of color yes you're going you know I feel one negotiates these spaces and then at some point you do make decisions and there are things that are not tenable but often that decision is not made in the moment of the act so another question how do we acknowledge that our historical selves are in the room when our entire relationship is based on agreeing to pretend that only our self selves are in the room that only our self selves exist for us well I think I you know I think that we need to pay attention to what we say I had a really embarrassing moment I was giving a embarrassing moment I was giving a talk with this at a college and this um this African-American student stood up and she said I read Citizen and and I understand why people like it but none of the stuff that happens to me is in your book and so I said well what kind of things happens to you and she said well for example you know when I was in high school my mom used to pick me up from school and bring me to my grandmother's house and she lived in a white neighborhood and um and then my mom went to work until midnight and at midnight she would come to my mother her grandmother's neighborhood to take her back to their house because the school that she attended was closer to where they lived and um and she said at least once a week the police would come and my mother would be on the floor and handcuffed and my grandmother would have to go outside and tell them that she's here to pick up her daughter and that happened a lot of times but I don't see any of that in your book and first of all it just broke my heart that that was her reality secondly it's not in the book because it was never my reality I never even knew that that was a possibility for a child just going to school while her mother her single mother worked I mean I know it intellectually but I didn't know it as a day-to-day kind of thing and it wouldn't have been in the book because the book specifically was about a certain kind of class relationship but still it felt like a moment where I had failed her so what was the question I forget so when we're in a room we um how do we acknowledge that our historical selves are there even though we try to feel it is only and so even though I understand historically how possible that dynamic is for her I know that I know that those things happen myself self Claudia in the world that's not my life and and I forgot to extend the book out to her like I forgot to move it into an arena where she would field held by citizen by virtue of holding scenarios or even asking people who have been in her position to tell me their stories so I think we're you know we're always coming up against the limits of her of ourselves as we negotiate intellectually our historical selves at least I find that for myself um and then the flip side are people who feel like their self is their historical self and I find that that's true often for white people they think I'm a good person so so historically whiteness is good and they can't separate the fact that there is a history and a reality that is not their actions even though their actions are made possible by that history and that reality um and you know so we I think we it's really about having a kind of consciousness about what is really the history not the history you want to have but what is really the history and how you as an individual negotiate spaces with that knowledge I mean I'm very conscious of my classes now about DACA and about students who might be undocumented I mean that's something I hadn't really thought aggressively about over the years and but now I cannot sit in the class I cannot make a list that does not include that as a possible scenario for someone in the class even though I don't know their particular histories even though that's something that goes un unnamed but I do I do think okay historically I know that this is possible for someone in this class and as an individual I want to be accountable to you so it's you know it's a it's a and we're always gonna leave things out that's why I told that story earlier we're all always gonna fail we are gonna fail we're gonna fail as human beings by definition the word human being means to fail I mean not really but but by by experience we know this is true and so yeah it's there's no answer to this question I guess is what I'm saying I think we're constantly negotiating and coming up against the limits of of what is institutionally true and what we want for ourselves in our interactions with others in the world yeah I mean one of the things that's been so interesting in that question I guess for me as somebody who's been traveling with you and talking about the play and being in rooms and rehearsing in various workshops and different audiences and I think this is going to sound ridiculous I suppose but I'm always surprised at how unaware people are of their of their historical selves and I have said kind of jokingly a number of times like I don't understand in particular why white men don't at least fake knowledge of their historical selves when we're talking about this play and in a weird way like they take over rooms they're the first to say something in the talk but like there there's a kind of lack of awareness of historical self that has taken me by surprise because the play is literally kind of putting it in your face or the book is kind of putting in your face and that would you know for me it gives me sort of a pause I think I'll pause and and think about that and I think whiteness my experience at least again in this in this context has been that white people very rarely take a count of themselves historically and people of color much more often think about it so and that has it surprised me because I like I said I I think oh at least fake like you would like fake it like you know be quiet or something and it doesn't it doesn't have but then but then you wouldn't be a white man you know like yeah like that you know it's it's been great you know I've been married for 25 years and my husband is six two blue-eyed previously blonde hair man when he had hair and it's been it's really kind of sometimes I just marvel at the way in which he can just move through the world and how people and not just other white people black people too are like welcome come in thank you for being here it's it's it's incredible it's really it's it's really so no wonder I mean not my husband my husband is very conscious of his his privilege but um it's no wonder that some men don't question because the world you know it's like I have had situations where we've been on vacation and like you know the Caribbean and and the black staff will treat me they'll give me like a broken chair to go on the beach but when my husband comes down suddenly he's over there in a cabana I'm like I need to travel with you apparently I need to like I can't go earlier because then I'm gonna get the broken chair um and this this from other black people so you know I think I think if if if white men um are feeling their power it's because they have the power another question uh from the book club uh let's talk about what happened after citizen what shifted for you after after the book well I think um you know I wrote citizen and I was thinking a lot about how do you how do you make tangible things that are invisible to many people um even you know even sometimes the black people um because you know after I wrote citizen I was in DC and this black woman older black woman came up to me and she said she said she wouldn't look at me she just came up to me and she said I um Miss Rankin I wanna I read citizen and I want to apologize to you because you know for years I've been watching Serena Williams and I have felt embarrassed by her I have felt like she is just acting out in public and making black people look bad and it never occurred to me that she was responding to something that she was actually fighting for her life out there and I can't tell you how ashamed I was when I read your essay she actually hadn't read the one in Citizen she read the one in the New York Times first and then she read Citizen so you know I I think that there is I don't know I think that we are all struggling to come up to speed with our ability to empathize with other people and um and this I think is is when it comes to people of color I think they're we went through a generation this is why you know like that Black Panther movie even though it's not that I mean I shouldn't say that okay maybe I'll just restart that question sometimes you get talking and you say things but but I think that even though that that movie I have some questions about it let's put it that way um I think that this this sense of coming into a reality that has a history a real history and that you are using that history and know that history and are trying to keep it present as you are being yourselves and dealing with other people I think that that is probably the hardest thing and and we are kind of fucked up as a culture because the history has been suppressed for some of us for many of us no matter our race I don't you know I think this actually goes beyond race I think it's it's it's about um what we were taught in schools and do you know something really um interesting I just learned this you know that African-American museum that opened in Washington that everybody's like this is the greatest thing since sliced bread that museum was supposed to be a slavery museum speaking of history and they thought that was too depressing to call it a slavery museum and so the fact that it becomes an African-American museum is the compromise because we can take a history like that but we can't take a history that comes from slavery which is the history that we have to to think about I mean I'm a little bit rambling now but I this is what's wrong with my inside of my head it kind of kind of shoots all over the place when when I start thinking about any one thing you know speaking of that though in terms of the museum and then the brian stevensson piece that you and I read recently and then you quickly inserted some a piece of it in the play in the white card about a couple things that he says in that article one that African-American people have never been human and and that the other is that the north may have won the war this is a line that you quote him in the play the north may have won the war but the south won the narrative and I just wondered if you could you know expound on that a little bit because I think we were both just like it was you know so moved by it yeah well the thing about the right now I'm in a struggle that has nothing to do with the play um I was supposed to write a piece for the New York Times and I started over Christmas to write the piece and it was on afro pessimism and the idea is behind afro pessimism is that black people should not involve themselves in civic or social dynamics in the United States because anti black racism is part of the foundational structure of this country so that no matter what I say to you no matter who I am no matter what I do no matter what I write no matter what play you see ultimately I am not human to you and that that's what afro pessimism claims and so I one of the founders Frank Wilderson and I called him because I'm just gonna write this piece and I called him and I said I said do you really believe that do you believe that black people are not human and he said yeah I believe it and I said but I am human and you're an human so how can you make that statement he said well because white people are in power and they don't think you're human so you have no agency and I said but what about you you work for an institution you have a job you have a lot of agency he says I have it because it was given to me but it could be taken away from me I could be killed tomorrow because I'm black so how is that me being human and it really after that it was a very frustrating conversation with this man because we kept going back and forth he said Fanot says you know you know the gaze of the white man is the gaze that has turned you into something that is an object and I said yeah but I don't live through the gaze of the white man I I have a life I can be happy I can be sad I can have he said you're naive if you don't think that's how you're living and that's how the conversation went and I was supposed to write this article in aproposimism and so I was thinking a lot about the thing that really irritated me about him was he said that for that reason I don't vote he said I'm not interested in being involved in a civic and social system that does not recognize me and I said so you're telling you know people not to vote and he said I'm I'm telling people I don't vote you can do what you want and that phone call rattled me because when I went to write the piece for the times every point I tried to debate on the other side it came down that he was right he was right institutional racism mass incarceration what is the thing that just happened yesterday I forget which is it a federal or state law that an employer can deny you employment if you have dreadlocks a hairstyle people so brian stevenson to get back to your question the north won the war but the south won the narrative it the narrative is what has driven legislation it has driven mass incarceration in this country I was in Boston waiting for the train at at south station to go home and I didn't hear it this last time but the last time I was here it said it said if you see something say something but remember seeing something is not seeing a person it's seeing an action and I thought oh you have to remind your people because for them seeing a person is seeing something is seeing a thing I mean that's what it's at and it it's cognizant of the history where black people and people of color are not considered human so I think when you know that's why when I read that article by brian stevenson it's it's depressing but it's true the south won the narrative they won it and it has determined my possibilities in this life you know my daughter goes to a private school and she decided she was going to run for president and my husband and I when she told us over breakfast she said I'm running for president of class and my gut reaction was to say to her you're not going to win and I didn't do it but I said great sounds good and then my husband looked at me and and so I said to her hey if you win what happens and if you lose what happens she said if I win I'm president if I lose I'll run for something else and I felt better and then and then the results came and she came in second and I said to her so who won and she said I'm not going to say the name in case it's your kid but she she said the name a boy's name and I said oh you know him and she said uh he's football player I don't really know him I said what kind of football player is he is he like a tom cruise football player I don't even know what that means why did I say that I don't know and she says no he's he's tall and blonde and I said uh so how was the speech and she said it was good gave a good speech it was funny and I said well um how was it compared to your speech and she said well you know mom my speech was like I'm going to do this for you and I'm going to do this and I'm going to work hard but his speech was kind of funny it just like said stuck that was funny and I I laughed when he gave his speech and that was it that was the end of our conversation but then I was thinking about it and I realized that that guy who was probably a great kid he could make jokes because he was already assumed to be competent to be a leader to be in charge and my daughter had to go up there she came in second so she's still on the council so you know don't feel bad for her but um but she had to prove that she could actually do the job and that you know that it's a it's a silly little story but it is it is about that thing of having to prove that you're human that you're competent that you're capable that you're here and that guy didn't you know he didn't have to prove that he made a joke about I actually I can't tell you a joke because if I told you a joke and he was your kid you would know so I won't tell you the joke but um yeah so so the south one the narrative and it shows up again and again and again and again uh yeah I mean just kind of a final comment question as we're kind of running out of time but um you know one of the things that that we were talking a little bit about last week as we were in previews for the play having to contend with what I was talking about earlier about the believability of the of the white characters and we were having a kind of late night conversation about that I was with the director and you and I talked about it earlier in the day and trying to figure out one of the comments that was made in the play one of the comments that someone made was that um a good-hearted white philanthropist would not also be invested in the real estate of prisons and so we were trying to decide should we address that in some way or you know like how do we respond to the white resistance of the play and up on my you know news feed came an article from the washington post saying that um you know according to the economic indicators life has not gotten better for african-americans in this country in 50 years and and it was in that moment that I just you know texted you all and was like so there's this and that's why we're doing the play um and uh and so I you know I just I think uh you know you and I talked a little bit about that but I just wonder kind of you know in that world of black pessimism or you know where is the optimism in an in an article like that well I think um to go back to the other question about the likability and the probability of the characters in the play in real life I mean I think a lot of white people felt like um or they they use this idea that the wealth of the characters means the characters are not them and that um charles's um investments or the building of prisons is not something they would do and the reason it's there is because in fact if you have a 401k you many of the investments are clustered and if you start to take them apart we're all invested in everything so this idea that just because you can name the thing and you personally did not build it that means you're not culpable or invested seems to me like a limitation in the imaginative possibilities of reality um you know I when I read or when I go to theater I don't think if I don't line up exactly with that character then the character obviously has nothing to do with me I find that a really interesting way to um assess what's what what one is interacting with rather than um thinking about the metaphorical ramifications of any any construction in front of one which is not to say that I couldn't fail I mean I fail all the time so maybe it's it it is a um bad characterization that's also on the table but it's curious to me this notion that um if I am not standing in exactly in a mirror of myself then the thing is unbelievable and I I think white people um use that line of logic to temper their own discomfort you know I I don't want to have to look at that I have not been made to look at it anywhere else so why should I be made to look at it here um but if I I was on the I was on a panel once where we had to talk about whether or not we could divest from crude oil and as we talked to the financial guys and started picking apart the investment clusters crude oil was just the beginning of it everything was present everything so I offered that up to those who feel like prisons are too far from anything their folk their their investments would touch um but the other part of your question was optimism optimism optimism is that a word I mean you know I I where was it where was that election with the child molester alabama yeah I wrote more I mean I you know black women thank you very much you know I I I we live here we are here we have had a tradition of opposition in this country that is fantastic we everything from um occupy wall street to black lives matter to what is happening in parkland right now we have brian stevensson's work we have people on different fronts we have the willingness of of the people in this audience to contend with the structure that we live under so I I think I am fundamentally an optimistic person because I am a parent we live in this world there is not another world there is not another option we are here together shipwrecked together you know that's a emily dickinson poem by the way so I you know I I I think that it feels hopeless at times but I wouldn't be sitting here I could be watching the Oscars and I'm not I'm sitting here because I feel like our lives are in our hands we um you know we didn't believe I believed but many didn't believe that we were willing to hand over the efforts towards the inconstant efforts towards our democracy to a fascist regime and and and and we did it you know we did it and now that we did it we have to face it and we have to figure out what to do next and um if the word for that is optimism then I'll take it thank you very much


Hello friends, I am Nawal Emul working as an assistant professor in mechanical engineering department Valchan Institute of Technology, Solapur. In this video, we are going to see Sylab mattresses Learning outcome at the end of this session students will be able to perform basic matrix operations on Sylab Content of the video is Introduction Arithmetic operations for mattresses basic matrix operations Introduction a matrix in layman's language is tabular data arranged in rows and columns Let us see an example of a matrix a Matrix a with three rows and three columns This can be defined in Sylab in a single line with rows Separated by the semicolon in the previous video I have shown you how the Sylab vector or Row vector and the column vector is defined in Sylab. So here if you want to define a matrix, we need to Define in a single line with the rows separated by a semicolon So when you enter this in Sylab, you get output like this So we'll have a quick We'll take an input a is equal to a square bracket 11 comma 12 comma indicates it is in row Semicolon indicates it will shift in the second column 21 space you can give comma also 22 comma 23 then semicolon then 31 comma 32 comma 33 Bracket complete enter. So this is a Matrix a with three element three rows and three columns So any element of the matrix can be referred to by specifying its row and column indices If you want to access the second element of the first row We may refer to it as a 1 comma 2 that one refers row and this two refers column For example, these are the columns and these are the rows So here 1 comma 2 refers first row first row and second column here So if you want to specify or if you want to access to this second element So the function will be a 1 comma 2 So when you press a 1 comma 2 in a curly bracket, you get output as 12. We'll just check in Sylab here so a capital A because we have defined as capital A 1 comma 2 When you press enter, so it will be Access that is 12 the element 1 comma 2 position is shown here so next In the same way if you want to show the position of 2 comma 3 it will be 23. You can just check here a 2 comma 3 So here that is second row third column the element is 23 when you press enter you get the second row third element Next to overwrite any defined value we can simply reassign it by using a 2 comma 3 is equal to 0 you can assign any value to any element or any position So it is very simple. The output will be like this So the third second row third column is re overrided by 0 You can try this with name different numbers also. So a 2 comma 3 Should be assigned or should be equal to suppose 0 5 just press enter. So this third Second row third element. So this position is replaced by number five. You can try with different numbers Sorry, so a capital A 2 comma 3 is equal to 0 When you press enter, so 2 comma 3 is replaced as 0 you can try with different positions also for example a 1 comma 2 should be replaced with 3 Just press enter. So this 1 comma 2 that is first row and second column is replaced by number 3 You can replace any number with any position The command will be the we call matrix A in a round bracket. First we'll call row then column So the next arithmetic operators for matrix So basic arithmetic addition subtraction and multiplication are done on matrices in Sylab in exactly the same way as they are traditionally defined in mathematics These operations work only if the size of the matrix are compatible That is the size of the matrix should be same There only this basic mathematics are performed in case of addition and subtraction the matrices I have to be exactly the same dimension and in the case of multiplication also the matrix Should be of same dimensions Here I have defined two matrices A and B A and B I have done the addition of these two matrices That is I have taken in the third variable C A plus B matrix A added with matrix B The output would be this one three five seven nine This is basic what we do in a matrix addition. I just clear this all The out the command for clearing the console window is CLC Suppose I take an A matrix Is equal to One space to comma semicolon three space or comma four Enter the then I have taken semicolon four comma five just present that the B is defined So there are two matrix A and B Suppose if you want to add these two matrix in a new variable called C You can write C is equal to A plus B and just type enter You get the addition of these two matrices In the same way you can take A minus B and the Substraction operator you B uses minus just present that you get Substraction of matrix A and B So it is very simple So B minus A or A minus B you can perform any operation And multiplication also very easy A we use a strict sign or a strict symbol into B You get multiplication of the two vectors So pause the video for few seconds and think What all matrix operations you can perform on Sylab apart from this addition Substraction multiplication what you can perform Pause the video for few seconds and think on this Okay, so we'll discuss this question later on in the video. So basic matrix operations In this section, we shall see how to handle a matrix including a navigation through it in special ways And implementing common operations such as transpose inverse, etc One of these basic information about the matrix is its dimension For two dimensional matrix It is of the form m comma n where m is number of rows and n is number of columns as I have discussed in the previous video We can use size function So here size function is used in Sylab to determine the dimensions of a matrix as demonstrated below Suppose I have taken a matrix that is a matrix of three rows and three columns And when I use a function size of a The command or the function is size of a the output would be three And three that it shows three rows and three columns. So we'll perform this operation in Sylab So first I'll clear the console window Then I'll take a new matrix I'll just press enter. So when I type size of a And just press enter it shows three and three that has three rows and three columns So in the same way the function diagonal To finding the diagonal elements the function is di ag And curly bracket or drowned brackets. So the function di ag of matrix shows the diagonal elements To find the sum of diagonal elements The function is trace. So you need to remember trace is finding the sum of diagonal elements So trace of matrix a gives the sum of all diagonal elements The lower triangular matrix whose elements above diagonal elements are zero is obtained by using Try l that is try lower triangular So the function is try l of a it gives you the lower triangular matrix in the same manner you can go with Upper triangular matrix for upper triangular matrix. The function is try you And you can find the transpose of the matrix And it is very simple that is a dash gives you the transpose of the matrix So here if I want to find The diagonal di Ag diagonal of a and if I enter you get the Diagonal elements here and if you want to sum those diagonal element the command is trace Of a just press enter you'll get sum of all the diagonal elements And if you want to find the upper triangular matrix or lower triangular matrix the command or the function is Try l of matrix a so here Above the diagonal elements all the elements become zero in the same way. I can use try u of a Just press enter so diagonal elements below it becomes zero that is called upper triangular Matrix so you can find a inverse also just write a dash And enter it so your columns are converted into rows and your rows are converted into So these are the references I have used Thank you


Dear students, the amino acids have unique properties which contribute towards building the overall property of a protein after folding. So we continue to study these properties so that we can better understand the properties of the proteins. You know that some of the amino acids can be positively charged and some of them are negatively charged. So these charged states, they vary with the pH because at low pH a lot more protons would be available as opposed to a high pH. So the charged state of an amino acid is essentially the property of the R group. The property of the R group to accept protons or donate protons. So that is how the overall charge of an amino acid can be determined. For that we need to understand the concept of PK value. So the PK of charged amino acids is simply the pH at which half of the molecules of the amino acid are charged while the other half are not charged. So PK can be different for different amino acids. So any amino acid given a 100 molecules of that amino acid, if 50 of them are charged and 50 are not charged, then that pH will be the PK value for that amino acid. So the negatively charged amino acids, that is aspartic acid and glutamic acid, they have PK values of 3.9 and 4.2 while for the positively charged amino acid lysine, arginine and histidine PK values for the side chain are 10.5, 12.5 and 6. So this is a very important concept because it helps you to determine the charge on an amino acid at any given pH. If the pH is less than the PK value for an amino acid, the amine side group chain gains a proton and becomes positively charged, hence basic. As shown here in the figure that if a proton is added onto the amine group, then the overall charge is positive. So if the pH is less than PK, only then enough protons will be available to be added and give rise to a positively charged amine group. Dear students, what if the case is reversed? If pH is greater than PK for an amino acid, the carboxyl side chain loses a proton. As opposed to the previous case. So upon losing a proton, the carboxyl group obviously it becomes negatively charged and hence acidic. You can see here the overall charge of the carboxyl group is negative and this is only for a pH that is greater than the PK value. So these perturbations in the PK value, they will tell you how many charges an amino acid has and the state. So towards that an overview or a complete chart of these five amino acids is shown here. The pH is provided on the vertical axis here and it varies from 0 till 13 and here if you see in the red, we have the pH values which were the PK values for these amino acids. So once the pH is increased, then the charge state of each amino acid changes. For the positively charged amino acids, if the pH is reduced, the charge state will differ. So this is a very nice elaboration on the behavior of these charged states as the pH varies. So to conclude, depending upon the pH value, you can calculate the charge state of your amino acid. This is very helpful if you want to extrapolate it to the protein as well. So depending upon the amino acid in question, this charge may be positive or negative.