Further Research on Drazin Inverse Formulas for Anti-Triangular Block Matrices

Abstract

This paper is devoted to studying the Drazin inverse of some structured matrices under new restrictive conditions in the literature. Specifically, we focus mainly on the Drazin inverse of two types of anti-triangular block matrices. Moreover, some particular cases of these results are also considered. New representations for the Drazin inverse of an arbitrary block matrix are provided under certain conditions, extending recent results. Furthermore, a numerical example will be presented at the end.