| 矩阵方程的正交对称与正交反对称最小二乘解 |
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| 引用本文： | 彭向阳,胡锡炎,张磊. 矩阵方程的正交对称与正交反对称最小二乘解[J]. 工程数学学报, 2006, 23(6): 1048-1052 |
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| 作者姓名： | 彭向阳 胡锡炎 张磊 |
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| 作者单位： | 长沙学院信息与计算科学系,长沙,410003;湖南大学数学与计量经济学院,长沙,410082;湖南大学数学与计量经济学院,长沙,410082 |
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| 基金项目： | 国家自然科学基金(10571047)，湖南省教育厅资助科研项目 |
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| 摘 要： | 研究了正交对称矩阵与对称矩阵、正交反对称矩阵与反对称矩阵之间的关系,根据广义奇异值分解定理,获得了矩阵方程A~TXB=C的正交对称和正交反对称最小二乘解存在的充分必要条件,并导出了相应的通解表达式。
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| 关 键 词： | 矩阵方程 正交对称 正交反对称 最小二乘解 |
| 文章编号： | 1005-3085(2006)06-1048-05 |
| 收稿时间： | 2005-02-28 |
| 修稿时间： | 2005-02-28 |
The Orthogonal-symmetric or Orthogonal-anti-symmetric Least-square Solutions of the Matrix Equation |
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| PENG Xiang-yang,HU Xi-yan,ZHANG Lei. The Orthogonal-symmetric or Orthogonal-anti-symmetric Least-square Solutions of the Matrix Equation[J]. Chinese Journal of Engineering Mathematics, 2006, 23(6): 1048-1052 |
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| Authors: | PENG Xiang-yang HU Xi-yan ZHANG Lei |
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| Affiliation: | 1- Department of Information and Computing Science, ChangSha University, Changsha 410003 2- College of Mathematics and Econometrics, Hunan University, Changsha 410082 |
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| Abstract: | We derive the relationships between the orthogonal-symmetric and symmetric matrices,the orthogonal-anti-symmetric and anti-symmetric matrices.By applying the generalized singular value decomposition (GSVD) of matrices,we provide explicit expressions for the least square solutions of the orthogonal-symmetric and orthogonal-anti-symmetric matrices of the matrix equation A~TXB=C. |
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| Keywords: | matrix equation orthogonal-symmetric orthogonal-anti-symmetric least-square solution |
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