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    Singular Matrix

    Definition

    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. matrix type | OEIS | counts for n = 1, 2, ... (-1, 0, 1)-matrices | A057981 | 1, 33, 7875, 15099201, ... (-1, 1)-matrices | A057982 | 0, 8, 320, 43264, ... (0, 1)-matrices | A046747 | 1, 10, 338, 42976, ...

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