| 一类矩阵方程的Hermitian R-对称定秩解 |
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| 引用本文： | 付莹.一类矩阵方程的Hermitian R-对称定秩解[J].数学杂志,2014,34(2):243-250. |
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| 作者姓名： | 付莹 |
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| 作者单位： | 东莞职业技术学院基础课部, 广东 东莞 523808 |
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| 基金项目： | Supported by Scientific Research Fund of Dongguan Polytechnic (JGXM2012203) |
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| 摘 要： | 本文研究了矩阵方程AX = B 的Hermitian R-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.
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| 关 键 词： | 矩阵方程 Hermitian R-对称矩阵 最大秩 最小秩 最佳逼近解 |
| 收稿时间： | 2013/1/15 0:00:00 |
| 修稿时间： | 2013/5/29 0:00:00 |
THE HERMITIAN R-SYMMETRIC EXTREMAL RANK SOLUTIONS OF A MATRIX EQUATION |
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| FU Ying.THE HERMITIAN R-SYMMETRIC EXTREMAL RANK SOLUTIONS OF A MATRIX EQUATION[J].Journal of Mathematics,2014,34(2):243-250. |
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| Authors: | FU Ying |
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| Institution: | Department of Basic, Dongguan Polytechnic, Dongguan 523808, China |
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| Abstract: | The Hermitian R-symmetric 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 hermitian R-symmetric to the equation is obtained. The expressions of such solutions to this equation are also given when the solvability conditions are satisfied. In addition, corresponding minimal rank solution set to the equation and the explicit expression of the nearest matrix to a given matrix in the Frobenius norm are provided. |
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| Keywords: | matrix equation Hermitian R-symmetric matrix maximal rank minimal rank optimal approximate solution |
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