ECHELON is an interception and relay system developed to monitor electronic communication between countries of the world.
Specifically, a matrix is in row echelon form if. 1  all nonzero rows (rows with at least one nonzero element) are above any rows of all zeroes (all zero rows, if any, belong at the bottom of the matrix), and. In other words, a matrix is in column echelon form if its transpose is in row echelon form. Therefore only row echelon forms are considered in the remainder of this article. The similar properties of column echelon form are easily deduced by transposing all the matrices. The reduced row echelon form of a matrix may be computed by Gauss–Jordan elimination. Unlike the row echelon form, the reduced row echelon form of a matrix is unique and does not depend on the algorithm used to compute it. This is an example of a matrix in reduced row echelon form: Note that this does not always mean that the left of the matrix will be an identity matrix, as this example shows. In other words, a matrix is in column echelon form if its transpose is in row echelon form. Therefore only row echelon forms are considered in the remainder of this article. The similar properties of column echelon form are easily deduced by transposing all the matrices. By the end of the 20th century, the system referred to as ECHELON had allegedly evolved beyond its military and diplomatic origins, to also become ... a global system for the interception of private and commercial communications.. In 1988, the first disclosure of the ECHELON surveillance system originated from Margaret Newsham, a Lockheed employee. Newsham told a member of the U.S. Congress that the telephone calls of Strom Thurmond, a Republican U.S. senator, were being collected by the NSA. A matrix that has undergone Gaussian elimination is said to be in row echelon form or, more properly, reduced echelon form or row-reduced echelon form.. Such a matrix has the following characteristics: 1. All zero rows are at the bottom of the matrix. 2.  ECHELON is an interception and relay system developed to monitor electronic communication between countries of the world. It is a global system formed by the United States, Canada, Great Britain, Australia, and New Zealand.  A rectangular matrix is in row echelon form if it has the following four properties: 1  All nonzero rows are above any rows of all zeros. 2  Each leading entry of a row is in a column to the right of the leading entry of the row above it. This will make every row start with a 1. The matrix is now in row echelon form: All nonzero rows are above any rows of all zeros (there are no zero rows), each leading entry of a row is in a column to the right of the leading entry of the row above it and all entries in a column below a leading entry are zeros. Row echelon form means that Gaussian elimination has operated on the rows and column echelon form means that Gaussian elimination has operated on the columns. In other words, a matrix is in column echelon form if its transpose is in row echelon form. Therefore only row echelon forms are considered in the remainder of this article. The similar properties of column echelon form are easily deduced by transposing all the matrices. A matrix is in reduced row-echelon form if it meets all of the following conditions: A row of only zero entries is called a zero row and the leftmost nonzero entry of a nonzero row is a leading 1. A column containing a leading 1 will be called a pivot column.  Reduced Row Echelon Form. A matrix is in reduced row echelon form (rref) when it satisfies the following conditions. 1  The matrix satisfies conditions for a row echelon form. 2  The leading entry in each row is the only non-zero entry in its column. Row Echelon Form. A matrix is in row echelon form (ref) when it satisfies the following conditions. 1  The first non-zero element in each row, called the leading entry, is 1. 2  Each leading entry is in a column to the right of the leading entry in the previous row
https://en.wikipedia.org/wiki/Row_echelon_form https://en.wikipedia.org/wiki/Row_echelon_form https://en.wikipedia.org/wiki/Echelon_(signals_intelligence) http://mathworld.wolfram.com/EchelonForm.html http://www.qwhatis.com/what-is-echelon/ https://en.wikibooks.org/wiki/Linear_Algebra/Row_Reduction_and_Echelon_Forms https://en.wikipedia.org/wiki/Row_echelon_form http://linear.ups.edu/html/section-RREF.html http://stattrek.com/matrix-algebra/echelon-form.aspx
what is echelon