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).

matrix 1-inverse | matrix inverse | Moore-Penrose matrix inverse | pseudoinverse

DrazinInverse

Michael P. Drazin