# Singular Matrix

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## singular matrix

[′siŋ·gyə·lər ′mā·triks]
(mathematics)
A matrix which has no inverse; equivalently, its determinant is zero.

## Singular Matrix

a square matrix A = ǀǀaijǀǀ 1n of order n whose determinant is equal to zero—that is, whose rank is less than n. A matrix is singular if and only if there is a linear dependence between its rows and between its columns.

References in periodicals archive ?
However, lansvd can fail for matrices that are nearly rank deficient (problems 18 and 19, marked by "-") because of the inversion of a singular or nearly singular matrix R.
bar] is the interpretation of the smallest singular value of a matrix as the distance between the matrix and the nearest singular matrix, since this is precisely the concept needed to determine the nearness of a stable transfer function to an unstable one.
If the control problem comes from an ordinary differential equation, then E = I and if it comes from a differential-algebraic equation, then E is a singular matrix.
4 states that the effective condition number of the deflated preconditioned system corresponding to the singular matrix A decreases if we increase the number of deflation vectors.
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