The Generalized Reflexive Solution for a Class of Matrix Equations (AX=B, XC=D)

In this article, the generalized reflexive solution of matrix equations (AX=B, XC=D) is considered. With special properties of generalized 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 solved.