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

Authors

Xiezhang Li, Georgia Southern UniversityFollow

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-AA^D)B=O and C(I-AA^D)=O, where A^D is the Drazin inverse of A. The representations of the Drazin inverse M^D have been studied in the case where the generalized Schur complement, S=A-CA^DB, is either zero or nonsingular. In this paper, we develop a representation, under certain conditions, for M^D 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.

Recommended Citation

Li, Xiezhang. 2011. "A Representation for the Drazin Inverse of Block Matrices with a Singular Generalized Schur Complement." Applied Mathematics and Computations, 217 (18): 7531-7536. doi: 10.1016/j.amc.2011.02.061
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/88