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| 摘要: |
| 本文研究了矩阵方程AX=B的双对称最大秩和最小秩解问题.利用矩阵秩的方法,获得了矩阵方程AX=B有最大秩和最小秩解的充分必要条件以及解的表达式,同时对于最小秩解的解集合,得到了最佳逼近解. |
| 关键词: 矩阵方程 双对称矩阵 最大秩 最小秩 最佳逼近解 |
| DOI： |
| 分类号:O241.6 |
| 基金项目:Supported by Scientiflc Research Fund of Dongguan Polytechnic (2012a01) |
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| BISYMMETRIC MINIMAL RANK SOLUTIONS AND ITS OPTIMAL APPROXIMATION TO A CLASS OF MATRIX EQUATION |
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FENG Tian-xiang
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| Abstract: |
| In this paper, the Bisymmetric maximal and minimal rank solutions to the matrix equation AX=B and their optimal approximation are considered. By applying the matrix rank method, the necessary and sufficient conditions for the existence of the maximal and minimal rank solutions with Bisymmetric to the equation. The expressions of such solutions to this equation are also given when the solvability conditions are satisfied. In addition, in corresponding the minimal rank solution set to the equation, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm has been provided. |
| Key words: matrix equation bisymmetric matrix maximal rank minimal rank optimal approximate solution |
