华东师范大学学报(自然科学版) ›› 2006, Vol. 2006 ›› Issue (5): 47-50.

• 数学 统计学 • 上一篇    下一篇

广义极分解的扰动等式

沈冬梅1,2,魏木生1   

  1. 1. 华东师范大学 数学系, 上海 200062; 2. 南通大学 理学院, 江苏 南通 226007
  • 收稿日期:2005-02-10 修回日期:2005-06-03 发布日期:2006-09-25
  • 通讯作者: 魏木生

Perturbation Identities for the Generalized Polar Decomposition (Chinese)

SHEN Dong-mei 1,2 , WEI Mu-sheng 1   

  1. 1. Department of Mathematics, East China Normal University, Shanghai ; 200062, China; 2. School of Science, Nantong University, Nantong Jiangsu 226007, China
  • Received:2005-02-10 Revised:2005-06-03 Published:2006-09-25
  • Contact: WEI Mu-sheng

摘要： 研究m×n(m≧n),且秩为r的复矩阵A的广义极分解A=QH,其中Q为m×n次酉矩阵,H,为n× n,半正定矩阵; 利用奇异值分解的方法,给出了在任意酉不变范数下Q,和H的扰动等式.

关键词: 广义极分解, 扰动等式, 酉不变范数, 广义极分解, 扰动等式, 酉不变范数

Abstract: This paper studied the generalized polar decomposition of an m×n(m≧n)complex matrix A ith rank r as A=QH, where Q is a subunitary matrix and H a positive semidefinite matrix. By the method of singular value decomposition, the perturbation identities of Q and H under the unitarily invariant norms were
obtained.

Key words: unitarily invariant norms, perturbation identity, generalized polar decomposition, unitarily invariant norms, perturbation identity

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