on the hermitian r-conjugate solution of a system of matrix equations
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ID: 245376
2012
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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.
| Reference Key |
dong2012journalon
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|---|---|
| Authors | ;Chang-Zhou Dong;Qing-Wen Wang;Yu-Ping Zhang |
| Journal | Chemico-biological interactions |
| Year | 2012 |
| DOI |
10.1155/2012/398085
|
| URL | |
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