On the Hermitian -Conjugate Solution of a System of Matrix Equations

Chang-Zhou Dong, Qing-Wen Wang and Yu-Ping Zhang

Journal of Applied Mathematics, 2012, vol. 2012, 1-14

Abstract:

Let be an by nontrivial real symmetric involution matrix, that is, . An complex matrix is termed -conjugate if , where denotes the conjugate of . We give necessary and sufficient conditions for the existence of the Hermitian -conjugate solution to the system of complex matrix equations and present an expression of the Hermitian -conjugate solution to this system when the solvability conditions are satisfied. In addition, the solution to an optimal approximation problem is obtained. Furthermore, the least squares Hermitian -conjugate solution with the least norm to this system mentioned above is considered. The representation of such solution is also derived. Finally, an algorithm and numerical examples are given.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:398085

DOI: 10.1155/2012/398085

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