Journal of Applied Mathematics
Volume 2012 (2012), Article ID 504650, 17 pages
http://dx.doi.org/10.1155/2012/504650
Research Article

The Group Involutory Matrix of the Combinations of Two Idempotent Matrices

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

1College of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning 530006, China
2College of Mathematics and Computer Science, Bijie University, Guizhou 551700, China
3School of Mathematical Sciences, Monash University, Clayton Cambus, VIC 3800, Australia

Received 19 December 2011; Accepted 16 March 2012

Academic Editor: Mehmet Sezer

Copyright © 2012 Lingling Wu 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 discuss the following problem: when 𝑎 𝑃 + 𝑏 𝑄 + 𝑐 𝑃 𝑄 + 𝑑 𝑄 𝑃 + 𝑒 𝑃 𝑄 𝑃 + 𝑓 𝑄 𝑃 𝑄 + 𝑔 𝑃 𝑄 𝑃 𝑄 of idempotent matrices 𝑃 and 𝑄 , where 𝑎 , 𝑏 , 𝑐 , 𝑑 , 𝑒 , 𝑓 , 𝑔 ∈ ℂ and 𝑎 ≠ 0 , 𝑏 ≠ 0 , is group involutory.