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 2×2 (0, 1)-matrices: [0 | 0 0 | 0], [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 following table gives the numbers of singular n×n matrices for certain matrix classes.

determinant | ill-conditioned matrix | matrix inverse | nonsingular matrix | singular value decomposition