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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 ifA¯=RAR, 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 AX=C and XB=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

journal of applied mathematics

On the Hermitian<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>R</mml:mi></mml:mrow></mml:math>-Conjugate Solution of a System of Matrix Equations

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