| 线性流形上矩阵方程ATXA＝B的D对称解 |
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| 引用本文： | 李珍珠.线性流形上矩阵方程ATXA＝B的D对称解[J].广西科学院学报,2008,24(3):174-176. |
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| 作者姓名： | 李珍珠 |
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| 作者单位： | 湖南科技学院数学与计算科学系,湖南永州,425100 |
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| 摘 要： | 利用矩阵对的广义奇异值分解,给出线性流形上矩阵方程ATXA＝B存在D对称解的充要条件及其通解的表达式,并导出线性流形上矩阵方程ATXA＝B的D对称最小二乘解的表达式.
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| 关 键 词： | 矩阵方程 线性流形 广义奇异值分解 D对称矩阵 最小二乘解 |
| 收稿时间： | 2007/8/3 0:00:00 |
The D-symmetric Solutions of Matrix Equation ATXA=B on the Linear Manifold |
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| LI Zhen-zhu.The D-symmetric Solutions of Matrix Equation ATXA=B on the Linear Manifold[J].Journal of Guangxi Academy of Sciences,2008,24(3):174-176. |
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| Authors: | LI Zhen-zhu |
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| Institution: | LI Zhen-zhu(Department of Mathematics , Computational Science,Hunan University of Science , Engineering,Yongzhou,Hunan,425100,China) |
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| Abstract: | By applying the generalized singular value decomposition of a matrix pair,the necessary and sufficient conditions and the expressions for the D-symmetric solutions of matrix equation ATXA=B on the linear manifold are established.In addition,the least-squares solutions of ATXA=B with respect to D-symmetric matrix are derived. |
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| Keywords: | matrix equation linear manifold generalized singular value decomposition D-symmetric matrix least-squares solution |
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