| 一类矩阵方程组AX=B,XD=E的对称解与反对称解 |
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| 引用本文： | 郭丽杰,周硕.一类矩阵方程组AX=B,XD=E的对称解与反对称解[J].吉林大学学报(理学版),2015,53(2):206-212. |
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| 作者姓名： | 郭丽杰 周硕 |
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| 作者单位： | 东北电力大学 理学院, 吉林 吉林 132012 |
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| 基金项目： | 国家自然科学基金(批准号:11072085);吉林省自然科学基金(批准号:201115180) |
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| 摘 要： | 考虑矩阵方程组AX=B,XD=E的对称解与反对称解,利用对称(反对称)矩阵的性质和矩阵对的标准相关分解(CCD),给出了矩阵方程组对称解(反对称解)存在的充分必要条件及解的一般表达式,并讨论了对任意给定矩阵的最佳逼近问题.
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| 关 键 词： | 矩阵方程组 对称矩阵 反对称矩阵 最佳逼近 标准相关分解 |
| 收稿时间： | 2014-06-24 |
Symmetric Solution and Anti symmetric Solution for aClass of Matrix Equations AX=B,XD=E |
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| GUO Lijie
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ZHOU Shuo.Symmetric Solution and Anti symmetric Solution for aClass of Matrix Equations AX=B,XD=E[J].Journal of Jilin University: Sci Ed,2015,53(2):206-212. |
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| Authors: | GUO Lijie ZHOU Shuo |
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| Institution: | College of Science, Northeast Dianli University, Jilin 132012, Jilin Province, China |
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| Abstract: | The symmetric solution and the anti symmetric solution of matrix equations AX=B, XD=E were considered. Based on the special properties of symmetric
(anti-symmetric) matrices and the canonical correlation decomposition (CCD) of a pair of matrices, the necessary and sufficient conditions for the solvability
and the general expression of the symmetric solution (anti symmetric solution) were obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set was solved. |
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| Keywords: | matrix equations symmetric matrix anti-symmetric matrix optimal approximation canonical correlation decomposition (CCD) |
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