Solving Optimization Problems on Hermitian Matrix Functions with Applications

Xiang Zhang and Shu-Wen Xiang

Journal of Applied Mathematics, 2013, vol. 2013, 1-11

Abstract:

We consider the extremal inertias and ranks of the matrix expressions , where , and are known matrices and and are the solutions to the matrix equations , , and , respectively. As applications, we present necessary and sufficient condition for the previous matrix function to be positive (negative), non-negative (positive) definite or nonsingular. We also characterize the relations between the Hermitian part of the solutions of the above-mentioned matrix equations. Furthermore, we establish necessary and sufficient conditions for the solvability of the system of matrix equations , , , and , and give an expression of the general solution to the above-mentioned system when it is solvable.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:593549

DOI: 10.1155/2013/593549

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