- reduced echelon matrix
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English-Finnish mathematical dictionary. 2011.
English-Finnish mathematical dictionary. 2011.
Matrix (mathematics) — Specific elements of a matrix are often denoted by a variable with two subscripts. For instance, a2,1 represents the element at the second row and first column of a matrix A. In mathematics, a matrix (plural matrices, or less commonly matrixes)… … Wikipedia
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
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
Elementary matrix — In mathematics, an elementary matrix is a simple matrix which differs from the identity matrix in a minimal way. The elementary matrices generate the general linear group of invertible matrices, and left (respectively, right) multiplication by an … 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
Reduction (mathematics) — In mathematics, reduction refers to the rewriting of an expression into a simpler form. For example, the process of rewriting a fraction into one with the smallest whole number denominator possible (while keeping the numerator an integer) is… … Wikipedia
Index calculus algorithm — In group theory, the index calculus algorithm is an algorithm for computing discrete logarithms. This is the best known algorithm for certain groups, such as mathbb{Z} m^* (the multiplicative group modulo m ).Dubious|date=April 2008 Description… … Wikipedia
Hermite normal form — In linear algebra, the Hermite normal form is a special form of reduced echelon form over the integers mathbb{Z}. Specifically, a matrix M over mathbb{Z} is said to be in Hermite normal form (often abbreviated HNF) if* It is upper triangular *… … 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
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