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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. |
| 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 |
| DOI： |
| 分类号:O241.6 |
| 基金项目: |
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| CENTRO-SYMMETRIC MINIMAL RANK SOLUTIONSAND ITS OPTIMAL APPROXIMATION OF THEMATRIX EQUATION AX=B |
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XIAO Qing-feng,HU Xi-yan,ZHANG Lei
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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. |
| Key words: matrix equation centro-symmetric matrix maximal rank minimal rank optimal approximate solution |
