On the Hermitian R‐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, issue 1

Abstract: Let R be an n by n nontrivial real symmetric involution matrix, that is, R = R−1 = RT ≠ In. An n × n complex matrix A is termed R‐conjugate if A¯=RAR, where A¯ denotes the conjugate of A. We give necessary and sufficient conditions for the existence of the Hermitian R‐conjugate solution to the system of complex matrix equations AX = C and XB = D and present an expression of the Hermitian R‐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 R‐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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https://doi.org/10.1155/2012/398085

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2012:y:2012:i:1:n:398085

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