| 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. |
| 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 |
| DOI： |
| 投稿时间：2007-08-03 |
| 基金项目: |
|
| The D-symmetric Solutions of Matrix Equation ATXA=B on the Linear Manifold |
|
LI Zhen-zhu
|
| (Department of Mathematics and Computional Science, Hunan University of Science and Engineering, Yongzhou, Hunan, 425100, China) |
| 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. |
| Key words: matrix equation linear manifold generalized singular value decomposition D-symmetric matrix least-squares solution |
