invertible matrix | regular 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. For example, there are 6 nonsingular 2×2 (0, 1)-matrices: [0 | 1 1 | 0], [0 | 1 1 | 1], [1 | 0 0 | 1], [1 | 0 1 | 1], [1 | 1 0 | 1], [1 | 1 1 | 0]. The following table gives the numbers of nonsingular n×n matrices for certain matrix classes. matrix type | OEIS | counts for n = 1, 2, ... (-1, 0, 1)-matrices | A056989 | 2, 48, 11808, ... (-1, 1)-matrices | A056990 | 2, 8, 192, 22272, ... (0, 1)-matrices | A055165 | 1, 6, 174, 22560, ...

determinant | diagonalizable matrix | invertible matrix theorem | matrix inverse | singular matrix