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| 矩阵方程XTAX=B的反对称正交对称解及其最佳逼近 | |
| 引用本文： | 吴彦良,尤传华,马军生.矩阵方程XTAX=B的反对称正交对称解及其最佳逼近[J].甘肃科学学报,2007,19(3):26-30. |
| 作者姓名： | 吴彦良 尤传华 马军生 |
| 作者单位： | 1. 中国酒泉卫星发射中心,甘肃,酒泉,732750 2. 兰州大学,数学与统计学院,甘肃,兰州,730000 3. 西安通信学院一系,陕西,西安,710106 |
| 摘 要： | 讨论了矩阵方程XTAX=B具有反对称正交对称矩阵解的充要条件,给出了通解的表达式.同时对给定的矩阵,求出了矩阵方程的最佳逼近解. |
| 关 键 词： | 矩阵方程 反对称正交对称矩阵 最佳逼近 |
| 文章编号： | 1004-0366（2007）03-0026-05 |
| 收稿时间： | 2006-08-08 |
| 修稿时间： | 2006-08-08 |
The Anti-symmetric Ortho-symmetric Solutions of Matrix Equation XTAX=B and Its Optimal Approximation |
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| WU Yan-liang,YOU Chuan-hua,MA Jun-sheng.The Anti-symmetric Ortho-symmetric Solutions of Matrix Equation XTAX=B and Its Optimal Approximation[J].Journal of Gansu Sciences,2007,19(3):26-30. | |
| Authors: | WU Yan-liang YOU Chuan-hua MA Jun-sheng |
| Abstract: | The necessary and sufficient condition for matrix equation X^TAX= B having anti-symmetric ortho-symmetric solutions are considered. The expression for general solutions is given. In addition, the expression of the optimal approximation solution to a given matrix is also provided. |
| Keywords: | matrix equation anti-symmetric ortho-symmetric matrices optimal approximation |
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