The Reflexive Solutions for a Pair of Simultaneous Linear Matrix Equations

摘要

In this paper, the reflexive solutions of a pair of matrix equations (AX = B, XC = D) is discussed. By applying special properties of reflexive matrices, we obtain the necessary and sufficient conditions for the existence of the solutions. We also derive a general form of the solutions. In addition, the unique optimal approximate solution is given by applying the properties of orthogonal projection matrices.