Abstract
In this paper, The Hermitian reflexive solutions and the anti-Hermitian reflexive solutions of matrix equations AX = B, XC = D are considered. With special properties of partitioned matrices and Hermitian reflexive (anti-Hermitian reflexive) matrices, the necessary and sufficient conditions for the solvability and the general expression of the solution are obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set is considered.
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