Extending EP matrices by means of recent generalized inverses (Q6590662)

A square complex matrix is called EP if it commutes with its Moore-Penrose inverse. The authors define a new class of matrices based on equalities of the form \(A^mX = XA^m\), where \(X\) is an outer generalized inverse of \(A\) and \(m\) is any positive integer. Using the core-EP decomposition, they provide characterizations for this new class of matrices and also derive a novel characterization of the Drazin inverse.\N\NMoreover, the authors obtain a new characterizations of \(k\)-EP matrices, \(k\)-DMP matrices, and dual \(k\)-DMP matrices.