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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 961568, 6 pages
http://dx.doi.org/10.1155/2013/961568
Research Article

The Optimization on Ranks and Inertias of a Quadratic Hermitian Matrix Function and Its Applications

Department of Mathematics, Shanghai University, Shanghai 200444, China

Received 3 December 2012; Accepted 9 January 2013

Academic Editor: Yang Zhang

Copyright © 2013 Yirong Yao. 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 solve optimization problems on the ranks and inertias of the quadratic Hermitian matrix function subject to a consistent system of matrix equations and . As applications, we derive necessary and sufficient conditions for the solvability to the systems of matrix equations and matrix inequalities , and in the Löwner partial ordering to be feasible, respectively. The findings of this paper widely extend the known results in the literature.