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:
The following table gives the numbers of singular matrices for certain matrix classes.
matrix type | OEIS | counts for ,
2, ... |
-matrices | A057981 | 1, 33, 7875, 15099201, ... |
-matrices | A057982 | 0, 8, 320, 43264,
... |
-matrices | A046747 | 1, 10, 338, 42976, ... |
See also
Determinant,
Ill-Conditioned Matrix,
Matrix Inverse,
Nonsingular
Matrix,
Singular Value Decomposition
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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 Matrix
Cite this as:
Weisstein, Eric W. "Singular Matrix."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SingularMatrix.html
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