| 矩阵方程AX=B,XD=E解的研究 |
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| 引用本文： | 盛兴平,陈果良.矩阵方程AX=B,XD=E解的研究[J].兰州大学学报(自然科学版),2006,42(3):101-104. |
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| 作者姓名： | 盛兴平 陈果良 |
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| 作者单位： | 1. 阜阳师范学院,数学系,安徽,阜阳,236032;华东师范大学,数学系,上海,200062
2. 华东师范大学,数学系,上海,200062 |
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| 基金项目： | 中国科学院资助项目，安徽省高校"优秀青年教师资助计划"，阜阳师范学院校科研和教改项目 |
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| 摘 要： | 详细讨论了矩阵方程AX=B,XD=E的各种解,即在相容时的极小范数解;在不相容时分两种情况讨论了最小二乘解,并分别给出了它们解的表达式;最后给出了该矩阵方程在不相容时的极小范数最小二乘解.
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| 关 键 词： | 矩阵方程 极小范数解 最小二乘解 极小范数最小二乘解 |
| 文章编号： | 0455-2059（2006）03-0101-04 |
| 收稿时间： | 2005-01-20 |
| 修稿时间： | 2005-01-20 |
Research to the solution of matrix equation AX = B, XD = E |
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| SHENG Xing-ping,CHEN Guo-liang.Research to the solution of matrix equation AX = B, XD = E[J].Journal of Lanzhou University(Natural Science),2006,42(3):101-104. |
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| Authors: | SHENG Xing-ping CHEN Guo-liang |
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| Institution: | 1. Department of Mathematics, Fuyang Normal College, Fuyang 236032, Anhui, China; 2. Department of Mathematics, East Normal University, Shanghai 200062, China |
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| Abstract: | In this paper all kinds of solutions for the matrix equation AX = B, XD = E are studied in detail. If the matrix equation AX = B, XD = E is consistent, we give the expression of its minimum-normal solution. If the matrix equation AX = B, XD = E is not consistent, we study its least-squares solution and express its least-squares solution in two cases. Finally we give the minimum-normal and least-squares solution to the matrix equation AX = B, XD = E in inconsistency. |
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| Keywords: | matrix equation minimum-normal solution least-squares solution minimmn-normal leastsquares solution |
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