Invertible matrix

In mathematics and especially linear algebra, an n-by-n matrix A is called invertible, non-singular or regular if there exists another n-by-n matrix B such that

Related Topics:
Mathematics - Linear algebra - Matrix

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:AB = BA = In,

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where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. 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. A square matrix that is not invertible is called singular. While the most common case is that of matrices over the real or complex numbers, all these definitions can be given for matrices over any ring.

Related Topics:
Identity matrix - Matrix multiplication - Real - Complex - Ring

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