Journal of Applied Mathematics
Volume 2013 (2013), Article ID 247028, 10 pages
Research Article

New Representations of the Group Inverse of Block Matrices

College of Science, Guangxi University for Nationalities, Nanning 530006, China

Received 13 March 2013; Accepted 25 June 2013

Academic Editor: Mehmet Sezer

Copyright © 2013 Xiaoji Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents a full rank factorization of a block matrix without any restriction concerning the group inverse. Applying this factorization, we obtain an explicit representation of the group inverse in terms of four individual blocks of the partitioned matrix without certain restriction. We also derive some important coincidence theorems, including the expressions of the group inverse with Banachiewicz-Schur forms.