Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 312767, 13 pages
doi:10.1155/2010/312767
Research Article

Further Results on the Reverse Order Law for {1,3}-Inverse and {1,4}-Inverse of a Matrix Product

Deqiang Liu and Hu Yang

College of Mathematics and Statistics, Chongqing University, Chongqing 400030, China

Received 28 October 2009; Accepted 16 April 2010

Academic Editor: Panayiotis Siafarikas

Copyright © 2010 Deqiang Liu and Hu Yang. 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

Both Djordjević (2007) and Takane et al. (2007) have studied the equivalent conditions for B{1,3}A{1,3}⊆(AB){1,3} and B{1,4}A{1,4}⊆(AB){1,4}. In this note, we derive the necessary and sufficient conditions for B{1,3}A{1,3}⊇(AB){1,3}, B{1,4}A{1,4}⊇(AB){1,4}, B{1,3}A{1,3}=(AB){1,3} and B{1,4}A{1,4}=(AB){1,4}.