Nonsingular Matrix
A square matrix that is not singular, i.e., one that has a matrix inverse. Nonsingular matrices are sometimes also called regular matrices. A square matrix is nonsingular iff its determinant is nonzero (Lipschutz 1991, p. 45). For example, there are 6 nonsingular 2×2 (0,1)-matrices:
![画像: [0 1; 1 0],[0 1; 1 1],[1 0; 0 1],[1 0; 1 1],[1 1; 0 1],[1 1; 1 0].](/index.cgi/larger-text/https://mathworld.wolfram.com/images/equations/NonsingularMatrix/NumberedEquation1.svg){kind=link}
The following table gives the numbers of nonsingular n×n matrices for certain matrix classes.
See also
Determinant, Diagonalizable Matrix, Invertible Matrix Theorem, Matrix Inverse, Singular MatrixExplore with Wolfram|Alpha
WolframAlpha
More things to try:
References
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.Lipschutz, S. "Invertible Matrices." Schaum's Outline of Theory and Problems of Linear Algebra, 2nd ed. New York: McGraw-Hill, pp. 44-45, 1991.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 A055165, A056989, and A056990 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Nonsingular MatrixCite this as:
Weisstein, Eric W. "Nonsingular Matrix." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NonsingularMatrix.html