| 一类矩阵方程的正交对称解及其最佳逼近 |
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| 引用本文： | 彭向阳,胡锡炎,张磊.一类矩阵方程的正交对称解及其最佳逼近[J].高等学校计算数学学报,2007,29(2):126-132. |
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| 作者姓名： | 彭向阳 胡锡炎 张磊 |
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| 作者单位： | 1. 长沙大学信息与计算科学系,长沙,410003
2. 湖南大学数学与计量经济学院,长沙,410082 |
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| 基金项目： | 国家自然科学基金资助(10571047)，湖南省教育厅资助科研项目． |
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| 摘 要： | 1引言设Rn×m表示所有n×m实矩阵集合,I表示单位矩阵,AT表示矩阵A的转置矩阵, ORn×n={P|PTP=I)表示列正交矩阵集,SORn×n={P|PT=P,P2=I}表示对称正交对称矩阵集．如无特别说明,本文中的矩阵P均指这类对称正交对称矩阵．在Rn×m上定义内积为
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| 关 键 词： | 矩阵方程 正交对称解 最佳逼近 充分必要条件 |
| 修稿时间： | 2005-03-22 |
THE ORTHOGONAL-SYMMETRIC SOLUTIONS OF THE MATRIX EQUATION AND THE OPTIMAL APPROXIMATION |
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| Peng Xiangyang,Hu Xiyan,Zhang Lei.THE ORTHOGONAL-SYMMETRIC SOLUTIONS OF THE MATRIX EQUATION AND THE OPTIMAL APPROXIMATION[J].Numerical Mathematics A Journal of Chinese Universities,2007,29(2):126-132. |
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| Authors: | Peng Xiangyang Hu Xiyan Zhang Lei |
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| Institution: | Department of Information and Computing Science of Changsha University,Changsha 410003;College of Mathematics and Econometrics, Hunan University, Changsha 410082 |
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| Abstract: | We derive the relation between the orthogonal-symmetric matrix and symmetric matrix. Applying the canonical correlations decomposition (CCD) of matrix pairs, we provide the necessary and sufficient conditions for the existence, and obtain the common expression of orthogonal symmetric solutions of matrix equation ATXB - C and the explicit expression of the optimal approximation solution to the given matrix in its corresponding solution set and minimum norm solution. |
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| Keywords: | matrix equation orthogonal symmetric matrices optimal approximation solution minimum norm solution |
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