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| 一类矩阵方程的埃尔米特自反最小二乘解 | |
| 引用本文： | 王江涛,张忠志,谢冬秀,雷秀仁.一类矩阵方程的埃尔米特自反最小二乘解[J].系统科学与数学,2010,30(8):1136-1147. |
| 作者姓名： | 王江涛 张忠志 谢冬秀 雷秀仁 |
| 作者单位： | 1. 华南理工大学理学院数学系,广州510640;华南理工大学工商管理学院,广州510640 2. 东莞理工学院数学系,东莞,523808 3. 北京信息科技大学理学院,北京,100085 4. 华南理工大学理学院,广州,510640 |
| 基金项目： | 国家自然科学基金，北京市教学名师建设 |
| 摘 要： | 利用埃尔米特自反矩阵的表示定理和矩阵的拉直方法,研究了矩阵方程$AX+BY=C$的埃尔米特自反最小二乘问题,进一步,给出了方程在埃尔米特自反矩阵集合中可解的充分必要条件,得到解的一般表达式,最后,对任意给定的一对复矩阵,得到了其相关最佳逼近问题解的表达式. |
| 关 键 词： | 埃尔米特自反矩阵 矩阵拉直 矩阵方程 最小二乘解 最佳逼近. |
| 收稿时间： | 2009-7-8 |
| 修稿时间： | 2010-7-8 |
THE LEAST-SQUARES SOLUTIONS WITH THE HERMITIAN-REFLEXIVE MATRIX FOR A CLASS OF MATRIX EQUATIONS |
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| WANG Jiangtao,ZHANG Zhongzhi,XIE Dongxiu,LEI Xiuren.THE LEAST-SQUARES SOLUTIONS WITH THE HERMITIAN-REFLEXIVE MATRIX FOR A CLASS OF MATRIX EQUATIONS[J].Journal of Systems Science and Mathematical Sciences,2010,30(8):1136-1147. | |
| Authors: | WANG Jiangtao ZHANG Zhongzhi XIE Dongxiu LEI Xiuren |
| Institution: | (1) Department of Mathematics, South China University of Technology, 510640;School of Business Administration,South China University of Technology,510640;(2)Department of Mathematics,Dongguan University of Technology,523808;(3)School of Sciences,Beijing Information Science and Technology University,100085;(4)Department of Mathematics, South China University of Technology, 510640 |
| Abstract: | By means of the properties of the Hermitian-reflexive matrix and the straightened matrix, this paper considers the least-squares solutions with Hermitian-reflexive for the matrix equation $AX+BY=C.$ The necessary and sufficient condition of the solutions for the matrix equation in the sets of Hermitian-reflexive matrices and the general expression of the solution are presented. Furthermore, for any two given complex matrices, the expression of the solution for relevant optimal approximate problem is derived. |
| Keywords: | Hermitian-reflexive matrix straightened matrix matrix equation least-squares solution optimal approximation |
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