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| 半正定极因子在酉不变范数下的绝对与相对扰动界 | |
| 引用本文： | 陈小山. 半正定极因子在酉不变范数下的绝对与相对扰动界[J]. 华南师范大学学报（自然科学版）, 2010, 1(3): 1-3 . |
| 作者姓名： | 陈小山 |
| 作者单位： | 华南师范大学数学科学学院,广东广州,510631 |
| 基金项目： | 国家自然科学基金资助项目，广东省自然科学基金资助项目 |
| 摘 要： | 设${bf A}={bf Q}{bf H}$是矩阵${bf A}in mathbb{bf C}^{mtimes n}$的极分解, 其中${bf Q}^{*}{bf Q}={bf I}$, ${bf I}$为$n$阶单位矩阵, ${bf H}$为$n$阶Hermite半正定矩阵. 给出了任意扰动下Hermite半正定极因子在酉不变范数下的绝对与相对扰动界. 对于满秩矩阵, 绝对与相对扰动界具有最优性质. |
| 关 键 词： | 极分解 酉不变范数 绝对与相对扰动界 |
| 收稿时间： | 2009-07-09 |
| 修稿时间： | 2009-12-02 |
THE ABSOLUTE AND RELATIVE PERTURBATION BOUNDS FOR THE HERMITIAN POSITIVE SEMIDEFINITE POLAR FACTOR UNDER UNITARILY INVARIANT NORM |
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| Chen Xiao-Shan. The Absolute and Relative Perturbation Bounds for the Hermitian Positive Semidefinite Polar Factor under unitarily invariant norm[J]. Journal of South China Normal University (Natural Science Edition), 2010, 1(3): 1-3 . | |
| Authors: | CHEN Xiaoshan |
| Abstract: | Let ${bf A}={bf Q}{bf H}$ be the polar decomposition of ${bf A}in {bf C}^{mtimes n}$, where ${bf Q}^{*}{bf Q}={bf I}$ is the $ntimes n$ identity, and ${bf H}$ is Hermitian positive semi-definite. The absolute and relative perturbation bounds of Hermitian positive semi-definite polar factor for the matrices with different ranks are presented under any unitarily invariant norm. The absolute and relative bounds for matrices with full ranks are optimal. |
| Keywords: | the polar decomposition unitarily invariant norm absolute and relative perturbation bounds |
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