| 一矩阵方程组的反射解 |
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| 引用本文： | 常海霞,王卿文.一矩阵方程组的反射解[J].上海大学学报(英文版),2007,11(4):355-358. |
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| 作者姓名： | 常海霞 王卿文 |
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| 作者单位： | Department of Mathematics College of Sciences,Shanghai University,Department of Mathematics,College of Sciences,Shanghai University,Shanghai 200444,P.R.China,Shanghai 200444,P.R.China |
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| 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.
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| 关 键 词： | 矩阵方程组 有限维中心代数 反函数 解题方法 |
| 收稿时间： | 9 October 2005 |
| 修稿时间： | 2005-10-09 |
Reflexive solution to a system of matrix equations |
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| CHANG Hai-xia,WANG Qing-wen.Reflexive solution to a system of matrix equations[J].Journal of Shanghai University(English Edition),2007,11(4):355-358. |
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| Authors: | CHANG Hai-xia WANG Qing-wen |
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| Institution: | Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China |
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| Abstract: | 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
‖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.
Project supported by the National Natural Science Foundation of China (Grant No.60672160) |
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| Keywords: | system of matrix equations Moore-Penrose inverse reflexive matrix antireflexive matrix Frobenius norm |
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