- reduced echelon form
- матем.приведённо-ступенчатая форма (матрицы)
English-Russian scientific dictionary. 2008.
reduced echelon form
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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
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
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
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
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
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
Reduction — Reduction, reduced, or reduce may refer to:cienceChemistry*Reduction – chemical reaction in which atoms have their oxidation number (oxidation state) changed. **Reduced gas – a gas with a low oxidation number **Ore reduction: see… … 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
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
