matrix inversion - vertaling naar russisch
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matrix inversion - vertaling naar russisch

SQUARE MATRIX WITH NON-ZERO DETERMINANT
Matrix inversion; Invertible Matrix Theorem; Invertible matrix theorem; Singular matrix; Non-singular matrix; Matrix inverse; Inverse of a matrix; Invertible matrices; Nonsingular; Nonsingular matrix; Invert matrix; Degenerate matrix; Degenerate metric; Invertible Matrix; Invertable matrix; Matrix 1-inverse; Reciprocal matrix; Matrix singularity; Invertibility; Inverse matrix; Singular matrices; Nonsingular matrices; Inverse matrices; Algorithms for matrix inversion; Blockwise inverse; Inverse Matrix

matrix inversion         

общая лексика

обращение матрицы

matrix inversion         
обращение матрицы
inverse matrix         

общая лексика

обратная матрица

Definitie

MATRIX MATH
<language> An early system on the UNIVAC I or II. [Listed in CACM 2(5):1959-05-16]. (1997-02-27)

Wikipedia

Invertible matrix

In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or nondegenerate), if there exists an n-by-n square matrix B such that

A B = B A = I n   {\displaystyle \mathbf {AB} =\mathbf {BA} =\mathbf {I} _{n}\ }

where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A, and is called the (multiplicative) inverse of A, denoted by A−1. Matrix inversion is the process of finding the matrix B that satisfies the prior equation for a given invertible matrix A.

A square matrix that is not invertible is called singular or degenerate. A square matrix with entries in a field is singular if and only if its determinant is zero. Singular matrices are rare in the sense that if a square matrix's entries are randomly selected from any bounded region on the number line or complex plane, the probability that the matrix is singular is 0, that is, it will "almost never" be singular. Non-square matrices (m-by-n matrices for which mn) do not have an inverse. However, in some cases such a matrix may have a left inverse or right inverse. If A is m-by-n and the rank of A is equal to n (nm), then A has a left inverse, an n-by-m matrix B such that BA = In. If A has rank m (mn), then it has a right inverse, an n-by-m matrix B such that AB = Im.

While the most common case is that of matrices over the real or complex numbers, all these definitions can be given for matrices over any ring. However, in the case of the ring being commutative, the condition for a square matrix to be invertible is that its determinant is invertible in the ring, which in general is a stricter requirement than being nonzero. For a noncommutative ring, the usual determinant is not defined. The conditions for existence of left-inverse or right-inverse are more complicated, since a notion of rank does not exist over rings.

The set of n × n invertible matrices together with the operation of matrix multiplication (and entries from ring R) form a group, the general linear group of degree n, denoted GLn(R).

Vertaling van &#39matrix inversion&#39 naar Russisch