| 线性流形上两类矩阵反问题的最小二乘解 |
| |
| 引用本文： | 梁茂林,代丽芳,何万生.线性流形上两类矩阵反问题的最小二乘解[J].纯粹数学与应用数学,2011,27(6):787-795. |
| |
| 作者姓名： | 梁茂林 代丽芳 何万生 |
| |
| 作者单位： | 天水师范学院数学与统计学院,甘肃天水,741001 |
| |
| 基金项目： | 甘肃省教育厅科研基金，天水师范学院科研基金 |
| |
| 摘 要： | 给定广义自反矩阵R,S,即R=R=R-1,S=S=S-1,若复矩阵X满足条件RXS=X（或RXS=X）,则称其为（R,S）-对称矩阵（或（R,S）-斜对称矩阵）.分别讨论了线性流形上（R,S）-对称矩阵和（R,S）-斜对称矩阵约束下矩阵方程MZN=E的最小二乘问题,得到了通解表达式.
|
| 关 键 词： | 矩阵方程 最小二乘解 广义自反矩阵 （R S）-对称矩阵 （R S）-斜对称矩阵 |
The least-squares solutions for two kinds of matrix inverse problems on linear manifolds |
| |
| LIANG Mao-lin,DAI Li-fang,HE Wan-sheng.The least-squares solutions for two kinds of matrix inverse problems on linear manifolds[J].Pure and Applied Mathematics,2011,27(6):787-795. |
| |
| Authors: | LIANG Mao-lin DAI Li-fang HE Wan-sheng |
| |
| Institution: | (School of Mathematics and Statistics,Tianshui Normal University,Tianshui 741001,China) |
| |
| Abstract: | Given generalized reflection matrices R,S,i.e.,R = R = R-1,S = S = S-1,we say that complex matrix X is（R,S）-symmetric（or（R,S）-skew symmetric） if RXS = X（or RXS = X）.In this paper,the least-squares problems of matrix equation MZN = E with（R,S）-symmetric and（R,S）-skew symmetric constraints on linear manifolds are investigated,and the general expressions of the solutions are obtained. |
| |
| Keywords: | matrix equation least-squares solution generalized reflection matrices （R S）-symmetric matrices （R S）-skew symmetric matrices |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
