Singular Matrix

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singular matrix

[′siŋ·gyə·lər ′mā·triks]
A matrix which has no inverse; equivalently, its determinant is zero.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
Since the singular matrix E is included in (39), the state vector x(k + 1) cannot be calculated directly when simulating.
Since TSLDA algorithm determines regularization parameters using cross-validation method, and it has high time complexity in eliminating singular matrix. Meanwhile, the full feature information in the four subspaces may not be entirely beneficial for classification, and it is necessary to extract superior feature vectors in the four projection spaces to improve the classification performance.
Thus, we consider that the Improved TSLDA using an approximate matrix method has eliminated the singular matrix and reduced the time complexity of the TSLDA effectively.
In the RED simulations, we were able to enhance the precision by projecting the diagonal matrix over second column of the left singular matrix.
Notably since [E.sub.n] is a singular matrix, which has at least one zero eigenvalue, [beta] cannot be equal to zero.
where [[??].sub.m1] is a nonsingular matrix and [[??].sub.m2] is a singular matrix whose eigenvalues are all null.
In most cases, the parameters of hypersonic technology systems change all the time, with derivative coefficient matrix into singular matrix; by [29] we describe the hypersonic technology systems as descriptor systems.
This is of particular importance in the case of optimal control problems for descriptor systems, where E is a singular matrix, [34], since typical numerical methods for computing optimal feedback controls require the pencils to be regular and of index at most one.
Corollary 4.4 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.
i.e., the null space for the singular matrix P([x.sub.0]).
Assume that [[PHI].sub.n]([z.sub.0]) is a singular matrix for [absolute value of [z.sub.0]] = 1.