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.
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.