A nonsingular matrix over a field is a square matrix with nonzero determinant. Equivalently, it is an invertible matrix.

For an integer matrix , the same condition makes invertible over the rational numbers , but need not have a matrix inverse with integer entries. It is invertible over the integers iff , in which case it is a unimodular matrix.

See also

Determinant, Integer Matrix, Invertible Matrix, Matrix Inverse, Unimodular Matrix

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Cite this as:

Weisstein, Eric W. "Nonsingular Matrix." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NonsingularMatrix.html

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