On the Hermitian R-Conjugate Solution of a System of Matrix Equations
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 com...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/398085 |
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| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |