Let be an by nontrivial real symmetric involution matrix, that is,. An complex matrix is termed -conjugate if, where denotes the conjugate of . We give necessary and sufficientconditions for the existence of the Hermitian -conjugate solution to the systemof complex matrix equations and present an expression ofthe Hermitian -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 -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.
"On the Hermitian -Conjugate Solution of a System of Matrix Equations." J. Appl. Math. 2012 (SI01) 1 - 14, 2012. https://doi.org/10.1155/2012/398085