Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 101085, 17 pages
doi:10.1155/2009/101085
Research Article

Trace Inequalities for Matrix Products and Trace Bounds for the Solution of the Algebraic Riccati Equations

Jianzhou Liu,1,2 Juan Zhang,2 and Yu Liu1

1Department of Mathematic Science and Information Technology, Hanshan Normal University, Chaozhou, Guangdong 521041, China
2Department of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, China

Received 25 February 2009; Revised 20 August 2009; Accepted 6 November 2009

Academic Editor: Jozef Banas

Copyright © 2009 Jianzhou 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

By using diagonalizable matrix decomposition and majorization inequalities, we propose new trace bounds for the product of two real square matrices in which one is diagonalizable. These bounds improve and extend the previous results. Furthermore, we give some trace bounds for the solution of the algebraic Riccati equations, which improve some of the previous results under certain conditions. Finally, numerical examples have illustrated that our results are effective and superior.