| THE GENERALIZED REFLEXIVE SOLUTION FOR A CLASS OF MATRIX EQUATIONS （AX- B, XC- D） |
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| 引用本文： | 李范良,胡锡炎,张磊.THE GENERALIZED REFLEXIVE SOLUTION FOR A CLASS OF MATRIX EQUATIONS （AX- B, XC- D）[J].数学物理学报(B辑英文版),2008,28(1):185-193. |
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| 作者姓名： | 李范良 胡锡炎 张磊 |
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| 作者单位： | [1]Institute of Mathematics and Physics, School of Sciences, Central South University of Forestry and Technology, Changsha 410004, China [2]College of Mathematics and Econometrics, Hunan University, Changsha 410082, China |
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| 基金项目： | This research was supported by National Natural Science Foundation of China （10571047）; and by Scientific Research Fund of Hunan Provincial Education Department of China Grant（06C235）; and by Central South University of Forestry and Technology （06Y017）; and by Specialized Research Fund for the Doctoral Program of Higher Education （20060532014） |
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| 摘 要： | 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.
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| 关 键 词： | 矩阵方程式 近似值 数学 求解方法 |
| 收稿时间： | 2005-09-21 |
| 修稿时间： | 2006-08-31 |
The Generalized Reflexive Solution for a Class of Matrix Equations (AX=B, XC=D) |
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| Li Fanliang, Hu Xiyan,Zhang Lei.The Generalized Reflexive Solution for a Class of Matrix Equations (AX=B, XC=D)[J].Acta Mathematica Scientia,2008,28(1):185-193. |
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| Authors: | Li Fanliang Hu Xiyan Zhang Lei |
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| Institution: | aInstitute of Mathematics and Physics, School of Sciences, Central South University of Forestry and Technology, Changsha 410004, China;bCollege of Mathematics and Econometrics, Hunan University, Changsha 410082, China |
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| Abstract: | 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. |
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| Keywords: | Matrix equations generalized reflexive matrix optimal approximation |
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