| 关于实方阵分解为一个正定阵与一个实对称阵的乘积 |
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| 引用本文： | 屠伯埙,王榕生. 关于实方阵分解为一个正定阵与一个实对称阵的乘积[J]. 安徽工业大学学报, 1987, 0(1) |
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| 作者姓名： | 屠伯埙 王榕生 |
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| 作者单位： | 复旦大学，华东冶金学院 |
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| 摘 要： | 实方阵 A 称为有 PS 分解,如果 A=PS,其中 P 是正定阵,S 是实对称阵。本文证明了 A 有 PS 分解的充要条件是,A 为阵。从而证明了实方阵 A 有 PS分解的充要条件是,A 相似于实对角阵。
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| 关 键 词： | PS分解 Колмогоров矩阵 Hermite 矩阵 ■H分解 |
On the Decomposition of a Real Matrix into a Positive Definite Matrix and Real Symmetric Matrix |
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| Tu Boxun. On the Decomposition of a Real Matrix into a Positive Definite Matrix and Real Symmetric Matrix[J]. Journal of Anhui University of Technology, 1987, 0(1) |
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| Authors: | Tu Boxun |
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| Affiliation: | Tu Boxun (Fudan University)Wang Rongsheng (East China Institute of Metallurgy) |
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| Abstract: | If a real matrix A is a product of a positive definite matrix P and a real symmetric matix S i.e.,A=PS,we say that A possesses a PS decomposi- tion,In this paper we prove the equavallence that A is a so-called matrix and A possesses a PS decomposi-tion,then we give a necessary and sufficient condition that A possesses a PS decomposition is that A is similar to real diagonal matrix. |
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