row echelon form

row echelon form
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English-Finnish mathematical dictionary. 2011.

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  • Row echelon form — In linear algebra a matrix is in row echelon form if * All nonzero rows are above any rows of all zeroes, and * The leading coefficient of a row is always strictly to the right of the leading coefficient of the row above it.This is the definition …   Wikipedia

  • Echelon — * ECHELON is an intelligence gathering network run by an international alliance of signals intelligence organizations known as UKUSA * The Echelon is the street publicity team of the band 30 Seconds to Mars, and also the name of a song on their… …   Wikipedia

  • Row equivalence — In linear algebra, two matrices are row equivalent if one can be changed to the other by a sequence of elementary row operations. Alternatively, two m times; n matrices are row equivalent if and only if they have the same row space. The concept… …   Wikipedia

  • Row space — In linear algebra, the row space of a matrix is the set of all possible linear combinations of its row vectors. The row space of an m times; n matrix is a subspace of n dimensional Euclidean space. The dimension of the row space is called the… …   Wikipedia

  • Euclidean subspace — In linear algebra, an Euclidean subspace (or subspace of R n ) is a set of vectors that is closed under addition and scalar multiplication. Geometrically, a subspace is a flat in n dimensional Euclidean space that passes through the origin.… …   Wikipedia

  • Gaussian elimination — In linear algebra, Gaussian elimination is an algorithm for solving systems of linear equations. It can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square… …   Wikipedia

  • Rank (linear algebra) — The column rank of a matrix A is the maximum number of linearly independent column vectors of A. The row rank of a matrix A is the maximum number of linearly independent row vectors of A. Equivalently, the column rank of A is the dimension of the …   Wikipedia

  • Column space — The column vectors of a matrix. In linear algebra, the column space of a matrix (sometimes called the range of a matrix) is the set of all possible linear combinations of its column vectors. The column space of an m × n matrix is a… …   Wikipedia

  • Kernel (matrix) — In linear algebra, the kernel or null space (also nullspace) of a matrix A is the set of all vectors x for which Ax = 0. The kernel of a matrix with n columns is a linear subspace of n dimensional Euclidean space.[1] The dimension… …   Wikipedia

  • Gauss–Jordan elimination — In linear algebra, Gauss–Jordan elimination is a version of Gaussian elimination that puts zeros both above and below each pivot element as it goes from the top row of the given matrix to the bottom. In other words, Gauss Jordan elimination… …   Wikipedia

  • System of linear equations — In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables. For example,:egin{alignat}{7}3x ; + ; 2y ; ; z ; = ; 1 2x ; ; 2y ; + ; 4z ; = ; 2 x ; + ; frac{1}{2} y ; ; z …   Wikipedia

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