[1]杨兴东,刘诗卉,涂媛媛.若干交换算子不等式(英文)[J].南京师范大学学报(自然科学版),2016,39(01):25.
 Yang Xingdong,Liu Shihui,Tu Yuanyuan.Some Inequalities for Commutators[J].Journal of Nanjing Normal University(Natural Science Edition),2016,39(01):25.
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若干交换算子不等式(英文)()
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《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

卷:
第39卷
期数:
2016年01期
页码:
25
栏目:
数学
出版日期:
2016-03-31

文章信息/Info

Title:
Some Inequalities for Commutators
作者:
杨兴东刘诗卉涂媛媛
南京信息工程大学数学与统计学院,江苏 南京 210044
Author(s):
Yang XingdongLiu ShihuiTu Yuanyuan
College of Mathematics & Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China
关键词:
特征值奇异值F-范数不等式交换算子
Keywords:
eigenvaluessingular valuesfrobenius norminequalitycommutator
分类号:
15A57,15A42
文献标志码:
A
摘要:
本文中设[Γ]和[Γ~]为m×n矩阵,A和B分别为m及n阶正规矩阵,利用矩阵特征值与奇异值性质,证明如下不等式:[σ||AI(r)m×n-I(r)m×nB||F≤||AΓ-ΓB~||F]. 同时,推广了相关文献的结论.
Abstract:
If [Γ] and [Γ~] are [m×n] diagonal matrces and A and B are normal matrices,then the upper bound of Frobenius norm of [AI(r)m×n-I(r)m×nB] should be [1σ||AΓ-ΓB~||F]. Some related inequalities are proved,and the results are generalized.

参考文献/References:

[1] LI R C. A perturbation bound for the generalized polar decomposition[J]. BIT Numerical Mathematic,1993,33:304-308.

[2] SUN J G,CHEN C H. Generalized polar decomsition[J]. Journal of computational mathematics,1989(3):262-273.
[3] MARSHALL A W,OLKIN I. Inequalities:theory of majoration and its applications[J]. New York:Academic Press,1979.
[4] WEISS G. The Fuglede commutativity theorem modulo the Hilbert-Schmidt class and generating functions for matrix operators,I,II[J]. Trans Amer Math Soc,1978,246:193-209.
[5] LI RCC. New perturbation bounds for the unitary polar factor[J]. SIAM J Matrix Annl Appl,1995,16:327-332.
[6] RAJENDRA R,CHANDLER D,FUAD K. Some inequalities for commutators and an applications to spectral variation[J]. Aequationes mathematicae,1991,41:70-78.
[7] DAVIS C,KAHAN W M. The rotation of eigenvectors by a perturbation[J]. SIAM J Numer Anal,1970(1):1-46.

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备注/Memo

备注/Memo:
Received data:2015-02-17. 
Foundation item:National Natural Science Foundation of China(40975037). 
Corresponding author:Yang Xingdong,professor,majored in numerical algebra. E-mail:xdyandnuist@163.com
doi:10.3969/j.issn.1001-4616.2016.01.004
更新日期/Last Update: 2016-03-30