| 矩阵方程AX=B的中心对称定秩解及其最佳逼近 |
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| 引用本文： | 肖庆丰,胡锡炎,张磊.矩阵方程AX=B的中心对称定秩解及其最佳逼近[J].数学杂志,2015,35(3):505-512. |
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| 作者姓名： | 肖庆丰 胡锡炎 张磊 |
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| 作者单位： | 东莞职业技术学院公共教学部, 广东 东莞 523808,湖南大学数学与计量经济学院, 湖南 长沙 410082,湖南大学数学与计量经济学院, 湖南 长沙 410082 |
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| 摘 要： | 本文研究了矩阵方程AX=B的中心对称解.利用矩阵对的广义奇异值分解和广义逆矩阵,获得了该方程有中心对称解的充要条件以及有解时,最大秩解、最小秩解的一般表达式,并讨论了中心对称最小秩解集合中与给定矩阵的最佳逼近解.
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| 关 键 词： | 矩阵方程 中心对称矩阵 最大秩解 最小秩解 最佳逼近解 |
| 收稿时间： | 2013/1/12 0:00:00 |
| 修稿时间： | 2013/5/25 0:00:00 |
CENTRO-SYMMETRIC MINIMAL RANK SOLUTIONSAND ITS OPTIMAL APPROXIMATION OF THEMATRIX EQUATION AX=B |
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| XIAO Qing-feng,HU Xi-yan and ZHANG Lei.CENTRO-SYMMETRIC MINIMAL RANK SOLUTIONSAND ITS OPTIMAL APPROXIMATION OF THEMATRIX EQUATION AX=B[J].Journal of Mathematics,2015,35(3):505-512. |
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| Authors: | XIAO Qing-feng HU Xi-yan and ZHANG Lei |
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| Institution: | Department of Basic, Dongguan Polytechnic, Dongguan 523808, China,College of Mathematics and Econometrics, Hunan University, Changsha 410082, China and College of Mathematics and Econometrics, Hunan University, Changsha 410082, China |
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| Abstract: | The centro-symmetric solutions of the matrix equation AX=B are considered. By using the generalized singular value decompositions of matrix pairs and generalized inverses of matrices, necessary and sufficient conditions for the existence of such solution and the expression of the maximal and minimal rank solutions are derived. Also, the optimal approximation for the minimal rand solution set to a given matrix is also discussed and the expression of the solution is presented. |
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| Keywords: | matrix equation centro-symmetric matrix maximal rank minimal rank optimal approximate solution |
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