Reflexive solution to a system of matrix equations

AbstractWe derive necessary and sufficient conditions for the existence and an expression of the (anti)reflexive solution with respect to the nontrivial generalized reflection matrix P to the system of complex matrix equations AX = B and XC = D. The explicit solutions of the approximation problem $$\mathop {\min }\limits_{X \in \phi } $$ ‖X − E‖F was given, where E is a given complex matrix and ϕ is the set of all reflexive (or antireflexive) solutions of the system mentioned above, and ‖·‖ is the Frobenius norm. Furthermore, it was pointed that some results in a recent paper are special cases of this paper.