A square procession that does not have actually a procession inverse. A matrix is singular iff that is determinant is 0. Because that example, there are 10 singular

(0,1)-matrices:

 ,<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>. " />

The adhering to table gives the numbers of singular

matrices for particular matrix classes.

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 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
REFERENCES:

Ayres, F.Jr. Schaum"s outline of Theory and also Problems the Matrices. Brand-new York: Schaum, p.39, 1962.

Faddeeva, V.N. ComputationalMethods of linear Algebra. Brand-new York: Dover, p.11, 1958.

Golub, G.H. And also Van Loan, C.F. MatrixComputations, 3rd ed. Baltimore, MD: Johns Hopkins, p.51, 1996.

Kahn, J.; Komlós, J.; and also Szemeredi, E. "On the Probability that a random

matrix is Singular." J. Amer. Math. Soc. 8, 223-240, 1995.

Komlós, J. "On the Determinant that

-Matrices." Studia Math. Hungarica 2, 7-21 1967.

Marcus, M. And also Minc, H. Introductionto linear Algebra. New York: Dover, p.70, 1988.

Marcus, M. And Minc, H. A inspection of matrix Theory and Matrix Inequalities. Brand-new York: Dover, p.3, 1992.

Sloane, N.J.A. Order A046747, A057981, and also A057982 in "The On-Line Encyclopedia of creature Sequences."

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