Nonsingular Matrix


Also found in: Dictionary, Thesaurus, Wikipedia.
Related to Nonsingular Matrix: symmetric matrix, Inverse of a matrix

nonsingular matrix

[′nän‚siŋ·gyə·lər ′mā·triks]
(mathematics)
A matrix which has an inverse; equivalently, its determinant is not zero.

Nonsingular Matrix

 

in mathematics, a square matrix A = ǀǀaijǀǀ1n of order n whose determinant \A\ is nonzero. Every nonsingular matrix is invertible. A nonsingular matrix defines a nonsingular linear transformation in n-dimensional space. The passage from one coordinate system to another is also defined by a nonsingular matrix.

References in periodicals archive ?
A nonsingular matrix B is a T + H Bezoutian if and only if its inverse [B.
T], then there exists a nonsingular matrix X [member of] [C.
n,n], this algorithm computes a real nonsingular matrix Y [member of] [R.
for some nonsingular matrix [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.
In Algorithm 2 we then determine a nonsingular matrix Z such that
The problem of selecting m columns from an m x n matrix A to form a structurally nonsingular matrix B is equivalent to finding a row-perfect matching in the bipartite graph of A.
As we have commented above, the triangular factors of the LDU-decomposition appearing when we apply complete pivoting to an n x n nonsingular matrix have off-diagonal elements with absolute value bounded above by 1 and then their condition numbers are bounded in terms of n.
1]) is an n x n (n [greater than or equal to] 2) nonsingular matrix diagonally dominant by rows and columns, then the LDU-decomposition of A satisfies [[kappa].
n]) [member of] M(D,E) with D a nonsingular matrix.
Notice that if D is a Hermitian and nonsingular matrix, then [mu] can be explicitly given (cf.
Given a nonsingular matrix A, and a matrix T such that [(I - T).
q(l,j)] is a nonsingular matrix, for all j, l, 1 [less than or equal to] j [less than or equal to] r, l = 0, 1, 2,.