| 线性流形上矩阵方程A^TXA=B的中心对称解 |
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| 引用本文： | 李珍珠.线性流形上矩阵方程A^TXA=B的中心对称解[J].工科数学,2008(5):132-137. |
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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： | 利用矩阵对的商奇异值分解，给出了线性流形上矩阵方程A^TXA=B存在中心对称解的充要条件及其通解的表达式.另外，导出了线性流形上矩阵方程的解集合中与给定矩阵的最佳逼近解的表达式.
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| 关 键 词： | 矩阵方程 线性流形 商奇异值分解 中心对称矩阵 |
The Centro-symmetric Solutions of Matrix Equation A^TXA=B on the Linear Manifold |
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| LI Zhen-zhu.The Centro-symmetric Solutions of Matrix Equation A^TXA=B on the Linear Manifold[J].Journal of Mathematics For Technology,2008(5):132-137. |
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| Authors: | LI Zhen-zhu |
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| Institution: | LI Zhen-zhu (Department of Mathematics and Computional Science, Hunan University of Science and Engineering, Yongzhou 425100, China) |
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| Abstract: | Using the quotie conditions for the existence and linear manifold are established nt singular value decomposition（QSVD） of matrix pairs, the necessary and sufficient the expressions for the centro-symmetric solutions of matrix equation A^TXA = B on the In addition, in the solution set of corresponding equation, the expression of the optimal approximation solution to given matrix is derived. |
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| Keywords: | matrix equation linear manifold quotient singular value decomposition eentro-symmetric matrix |
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