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2012 On the Hermitian R -Conjugate Solution of a System of Matrix Equations
Chang-Zhou Dong, Qing-Wen Wang, Yu-Ping Zhang
J. Appl. Math. 2012(SI01): 1-14 (2012). DOI: 10.1155/2012/398085


Let R be an n by n nontrivial real symmetric involution matrix, that is, R = R 1 = R T I n . An n × n complex matrix A is termed R -conjugate if A ¯ = R A R , where A ¯ denotes the conjugate of A . We give necessary and sufficientconditions for the existence of the Hermitian R -conjugate solution to the systemof complex matrix equations A X = C and X B = D and present an expression ofthe Hermitian R -conjugate solution to this system when the solvability conditionsare satisfied. In addition, the solution to an optimal approximation problem isobtained. Furthermore, the least squares Hermitian R -conjugate solution with theleast norm to this system mentioned above is considered. The representation ofsuch solution is also derived. Finally, an algorithm and numerical examples aregiven.


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Chang-Zhou Dong. Qing-Wen Wang. Yu-Ping Zhang. "On the Hermitian R -Conjugate Solution of a System of Matrix Equations." J. Appl. Math. 2012 (SI01) 1 - 14, 2012.


Published: 2012
First available in Project Euclid: 16 July 2013

zbMATH: 1268.15008
MathSciNet: MR3005189
Digital Object Identifier: 10.1155/2012/398085

Rights: Copyright © 2012 Hindawi


Vol.2012 • No. SI01 • 2012
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