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

[摘要] LetRbe annbynnontrivial real symmetric involution matrix, that is,R=R−1=RT≠In. Ann×ncomplex matrixAis termedR-conjugate ifA¯=RAR, whereA¯denotes the conjugate ofA. We give necessary and sufficientconditions for the existence of the HermitianR-conjugate solution to the systemof complex matrix equationsAX=C and XB=Dand present an expression ofthe HermitianR-conjugate solution to this system when the solvability conditionsare satisfied. In addition, the solution to an optimal approximation problem isobtained. Furthermore, the least squares HermitianR-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.

[学科分类] 应用数学