A square matrix that does not have a matrix inverse. A matrix is singular iff its determinant
is 0. For example, there are 10 singular 
(0,1)-matrices:
![[0 0; 0 0],[0 0; 0 1],[0 0; 1 0],[0 0; 1 1],[0 1; 0 0]
[0 1; 0 1],[1 0; 0 0],[1 0; 1 0],[1 1; 0 0],[1 1; 1 1].](/images/equations/SingularMatrix/NumberedEquation1.svg) |
The following table gives the numbers of singular 
matrices for certain matrix classes.
Singular Matrix
,
2, ...
-matrices
-matrices
-matricesSee also
Determinant, Ill-Conditioned Matrix, Matrix Inverse, Nonsingular Matrix, Singular Value DecompositionExplore with Wolfram|Alpha
References
Ayres, F. Jr. Schaum's Outline of Theory and Problems of Matrices. New York: Schaum, p. 39, 1962.Faddeeva, V. N. Computational Methods of Linear Algebra. New York: Dover, p. 11, 1958.Golub, G. H. and Van Loan, C. F. Matrix Computations, 3rd ed. Baltimore, MD: Johns Hopkins, p. 51, 1996.Kahn, J.; Komlós, J.; and Szemeredi, E. "On the Probability that a Random
Matrix is Singular." J. Amer.
Math. Soc. 8, 223-240, 1995.Komlós, J. "On the
Determinant of 
-Matrices."
Studia Math. Hungarica 2, 7-21 1967.Marcus, M. and Minc,
H. Introduction
to Linear Algebra. New York: Dover, p. 70, 1988.Marcus,
M. and Minc, H. A
Survey of Matrix Theory and Matrix Inequalities. New York: Dover, p. 3,
1992.Sloane, N. J. A. Sequences A046747,
A057981, and A057982
in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Singular MatrixCite this as:
Weisstein, Eric W. "Singular Matrix." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SingularMatrix.html