| 实方阵的对称与正交和分裂的存在性与惟一性 |
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| 引用本文： | 梁景伟.实方阵的对称与正交和分裂的存在性与惟一性[J].中国石油大学学报(自然科学版),2003,27(4). |
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| 作者姓名： | 梁景伟 |
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| 作者单位： | 石油大学数理系,北京,102249 |
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| 摘 要： | 证明了n阶实方阵的对称与正交和分裂定理 ,即在一定条件下 ,一个实方阵可以惟一地分裂成一个对称矩阵与一个正交矩阵之和 ,在更一般意义下 ,可惟一地分裂成一个对称矩阵与一个正交矩阵的常数倍之和。
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| 关 键 词： | 实方阵 分裂 对称矩阵 正交矩阵 奇异值 存在性 惟一性 |
Existence and uniqueness of decomposed sum of symmetric and orthogonal parts for a real square matrix |
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| LIANG Jing-wei.Existence and uniqueness of decomposed sum of symmetric and orthogonal parts for a real square matrix[J].Journal of China University of Petroleum,2003,27(4). |
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| Authors: | LIANG Jing-wei |
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| Institution: | LIANG Jing-wei. Department of Mathematics and Physics in the University of Petroleum,China,Beijing 102249 |
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| Abstract: | The decomposition principle of an n-square matrix decomposed into a sum of a symmetric part and an orthogonal part was proved. For any n-square matrix, it can be decomposed into a sum of a symmetric matrix and an orthogonal matrix uniquely under some conditions. In general, it can be decomposed into constant multiple sum of a symmetric matrix and an orthogonal matrix uniquely. |
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| Keywords: | real square matrix decomposition symmetric matrix orthogonal matrix singular value existence uniqueness |
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