摘要
We 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 min x∈Ф ｜｜X - E｜｜F was given, where E is a given complex matrix and Ф 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.
We 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 min x∈Ф ｜｜X - E｜｜F was given, where E is a given complex matrix and Ф 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.
基金
supported by the National Natural Science Foundation of China （Grant No.60672160）
