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| 矩阵方程组AX=C,XB=D的公共最小二乘解 | |
| 引用本文： | 刘永辉. 矩阵方程组AX=C,XB=D的公共最小二乘解[J]. 应用数学, 2007, 20(2): 248-252 |
| 作者姓名： | 刘永辉 |
| 作者单位： | 上海金融学院应用数学系,上海,201209;中国科学院数学与系统科学研究院,北京,100080 |
| 基金项目： | 上海市教委资助项目;中国博士后科学基金 |
| 摘 要： | 通过使用矩阵秩方法,我们给出了矩阵方程组AX =C,XB =D的公共最小二乘解的通解表达式,以及公共最小二乘解的极大秩和极小秩. |
| 关 键 词： | 矩阵方程组 极大秩 极小秩 公共最小二乘解 广义逆 |
| 文章编号： | 1001-9847(2007)02-0248-05 |
| 修稿时间： | 2006-04-29 |
The Common Least-square Solutions to the Matrix Equations AX=C, XB= D |
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| LIU Yong-hui. The Common Least-square Solutions to the Matrix Equations AX=C, XB= D[J]. Mathematica Applicata, 2007, 20(2): 248-252 | |
| Authors: | LIU Yong-hui |
| Affiliation: | 1. Department of Applied Mathematics, Shanghai Finance University, Shanghai 201209, China2. Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences,Chinese Academy of Sciences, Beijing 100080, China |
| Abstract: | By applying the matrix rank method,in this note,the general expressions of the common least-square solutions to the matrix equations AX=C,XB=D is deduced,the extremal ranks of the common least-square solutions is obtained. |
| Keywords: | Matrix equation Maximal rank Minimal rank Common least-square solution Generalized inverse |
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