Block Representations For The Drazin Inverse Of Anti-Triangular Matrices

The paper is devoted to the study of the Drazin inverse of some structured matrices that appear in applications. We focus mainly on deriving formulas for the Drazin inverse of an anti-triangular block matrix M in terms of its blocks. New representations for the Drazin inverse of M are given under some conditions, that extend recent results in the literature. Additionally, these results are applied to investigate the Drazin inverse of certain structured matrices, in particular the group inverse for Hermitian matrices, and to study additive properties of the Drazin inverse.