Further results on the representation of the Drazin inverse of a 2×2 block matrix

https://doi.org/10.1016/j.laa.2009.02.001Get rights and content
Under an Elsevier user license
open archive

Abstract

The aim of this paper is to establish an explicit representation of the Drazin inverse of a 2×2 block matrix M=ABCD, where A and D are square matrices, in terms of the Drazin inverses of A and D. First, we give a formula for the Drazin inverse of M with the blocks satisfying the conditions BC=0, BDC=0, and BD2=0. Further, we derive representations of the Drazin inverse of M under less restrictive conditions than those found in the current literature.

AMS

15A09

Keywords

Drazin inverse
Block matrix
Index

Cited by (0)

The research has been partly supported by Project MTM2007-67232, “Ministerio de Educación y Ciencia” of Spain.