The Drazin inverse is a matrix inverse-like object derived from a given square matrix. In particular, let the index k of a square matrix be defined as the smallest nonnegative integer such that the matrix rank satisfies rank(A^(k + 1)) = rank(A^k). Then the Drazin inverse is the unique matrix A^D such that A^(k + 1) A^D | = | A^k A^D A A^D | = | A^D A A^D | = | A^D A. If A is an invertible matrix with matrix inverse A^(-1), then A^D = A^(-1). The Drazin inverse is implemented in the Wolfram Language as DrazinInverse[m].
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