A square matrix is singular if and only if its determinant is 0. If A has rank m, then it has a right inverse: an n-by-m matrix B such that AB = I.Ī square matrix that is not invertible is called singular or degenerate. If A is m-by-n and the rank of A is equal to n, then A has a left inverse: an n-by-m matrix B such that BA = I. However, in some cases such a matrix may have a left inverse or right inverse. Non-square matrices do not have an inverse. It follows from the theory of matrices that ifįor finite square matrices A and B, then also ![]() ![]() If this is the case, then the matrix B is uniquely determined by A and is called the inverse of A, denoted by A−1. Where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. In linear algebra an n-by-n matrix A is called invertible if there exists an n-by-n matrix B such that Freebase (2.00 / 2 votes) Rate this definition:
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