| 矩阵方程AX=B的中心对称最小秩解及其最佳逼近 |
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| 引用本文： | 刘瑞娟,周富照. 矩阵方程AX=B的中心对称最小秩解及其最佳逼近[J]. 汕头大学学报(自然科学版), 2008, 23(1): 1-7 |
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| 作者姓名： | 刘瑞娟 周富照 |
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| 作者单位： | 长沙理工大学数学与计算科学学院,长沙,410076 |
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| 摘 要： | 利用矩阵对的商奇异值分解,得到了矩阵方程AX=B有中心对称解的充分必要条件,以及有解时,最小、最大秩解的一般表达式.另外,给出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 商奇异值分解 最小秩解 |
| 文章编号： | 1001-4217（2008）01-0001-07 |
| 收稿时间： | 2007-08-20 |
| 修稿时间： | 2007-08-20 |
Centro-Symmetric Minimal Rank Solutions of Matrix Equation AX=B and Its Optimal Approximation |
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| LIU Rui-juan,ZHOU Fu-zhao. Centro-Symmetric Minimal Rank Solutions of Matrix Equation AX=B and Its Optimal Approximation[J]. Journal of Shantou University(Natural Science Edition), 2008, 23(1): 1-7 |
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| Authors: | LIU Rui-juan ZHOU Fu-zhao |
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| Affiliation: | (Changsha University of Science and Technology, Changsha 410076, Hunan, China) |
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| Abstract: | By applying the quotient singular value decomposition of matrix pairs, the necessary and sufficient conditions are obtained for the existence of the eentro-symmetrie solutions of the matrix equation AX=B, and the expression of the minimal and maximal rank solutions is also shown. In addition, for the minimal rank solution set, the expression of the optimal approximation solution to a given matrix is derived. |
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| Keywords: | matrix equation centro-symmetrie matrix quotient singular value decomposition minimal rank solution |
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