Title

A Representation for the Drazin Inverse of Block Matrices with a Singular Generalized Schur Complement

Document Type

Article

Publication Date

5-15-2011

Publication Title

Applied Mathematics and Computations

DOI

10.1016/j.amc.2011.02.061

ISSN

0096-3003

Abstract

Consider a 2×2 block complex square matrix M=[ABCD], where A and D are square matrices. Suppose that (I-AAD)B=O and C(I-AAD)=O, where AD is the Drazin inverse of A. The representations of the Drazin inverse MD have been studied in the case where the generalized Schur complement, S=A-CADB, is either zero or nonsingular. In this paper, we develop a representation, under certain conditions, for MD when S is singular and group invertible. Moreover, this formula includes the case where S=O or nonsingular. A numerical example is given to illustrate the result.

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