Journal of Applied Mathematics
Volume 2011 (2011), Article ID 831892, 13 pages
http://dx.doi.org/10.1155/2011/831892
Research Article

On the Drazin Inverse of the Sum of Two Matrices

Xiaoji Liu,1,2 Shuxia Wu,1 and Yaoming Yu3

1College of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning 530006, China
2Guangxi Key Laboratory of Hybrid Computational and IC Design Analysis, Nanning 530006, China
3School of Mathematical Sciences, Monash University, Caulfield East, VIC 3800, Australia

Received 31 March 2011; Revised 25 August 2011; Accepted 21 October 2011

Academic Editor: Michela Redivo-Zaglia

Copyright © 2011 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.

Abstract

We deduce the explicit expressions for (P+Q)D and (PQ)D of two matrices P and Q under the conditions P2Q=PQP and Q2P=QPQ. Also, we give the upper bound of |P+QD-PD|2.