Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 620758, 18 pages
Research Article

New Trace Bounds for the Product of Two Matrices and Their Applications in the Algebraic Riccati Equation

Department of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, China

Received 25 September 2008; Accepted 19 February 2009

Academic Editor: Panayiotis Siafarikas

Copyright © 2009 Jianzhou Liu and Juan Zhang. 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.


By using singular value decomposition and majorization inequalities, we propose new inequalities for the trace of the product of two arbitrary real square matrices. These bounds improve and extend the recent results. Further, we give their application in the algebraic Riccati equation. Finally, numerical examples have illustrated that our results are effective and superior.