[1]杨兴东,苏润青,徐玮玮,等.Von Neumann迹的不等式注记[J].南京师范大学学报(自然科学版),2018,41(01):5.[doi:10.3969/j.issn.1001-4616.2018.01.002]
　Yang Xingdong,Su Runqing,Xu Weiwei,et al.A Note on Von Neumann’s Trace Inequality[J].Journal of Nanjing Normal University(Natural Science Edition),2018,41(01):5.[doi:10.3969/j.issn.1001-4616.2018.01.002]
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Von Neumann迹的不等式注记()
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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41卷
期数:
2018年01期
页码:
5
栏目:
·数学·
出版日期:
2018-03-31

文章信息/Info

Title:
A Note on Von Neumann’s Trace Inequality
文章编号:
1001-4616(2018)01-0005-04
作者:
杨兴东; 苏润青; 徐玮玮; 刘诗卉; 丁三芹
南京信息工程大学数学与统计学院,江苏 南京 210044
Author(s):
Yang Xingdong; Su Runqing; Xu Weiwei; Liu Shihui; Ding Sanqin
College of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China
关键词:
Von Neumann不等式; 特征值; 奇异值; 迹; Frobenius范数
Keywords:
Von Neumann inequality; eigenvalue; singular value; trace; Frobenius norm
分类号:
O151.21
DOI:
10.3969/j.issn.1001-4616.2018.01.002
文献标志码:
A
摘要:
通过矩阵分块,利用矩阵特征值与奇异值的性质,研究Von Neumann迹的不等式,推广了相关文献矩阵乘积之迹的不等式,并对有关文献作了补充.
Abstract:
In this paper,the inequality of Von Neumann trace was studied by using the properties of the matrix divided into blocks,singular value and eigenvalue of the matrix. As a result,the inequalities of the matrix product trace were improved under the certain conditions. Besides,the established conclusions were extended.

参考文献/References:

[1] VON NEUMANN J. Some matrix-inequalities and metrization of matric-space[J]. Tomsk Univ Rev,1937,1:286-300.
[2]MIRSKY L. On the trace of matrix products[J]. Mathematische nachrichten,1959,20(3/6):171-174.
[3]MIRSKY L. A trace inequality of John von Neumann[J]. Monatshefte für mathematik,1975,79(4):303-306.
[4]MARSHALL A W,OLKIN I,ARNOLD B. Inequalities:theory of majorization and its applications[M]. New York:Springer Science and Business Media,2010:66-300.
[5]BEN I A,GREVILLE T N E. Generalized inverses:theory and applications[M]. New York:Springer Science and Business Media,2003:227-229.
[6]HORN R A,JOHNSON C R. Matrix analysis[M]. New York:Cambridge University Press,2012:67-140.
[7]KOMAROFF N. Enhancements to the von Neumann trace inequality[J]. Linear algebra and its applications,2008(428):738-741.
[8]WILKINSON J H. The algebraic eigenvalue problem[M]. Oxford:Clarendon Press,1965:34-77.
[9]WEYL H. Inequalities between the two kinds of eigenvalues of a linear transformation[J]. Proceedings of the national academy of sciences of the United States of America,1949,35(7):408.
[10]BALL J M. Convexity conditions and existence theorems in nonlinear elasticity[J]. Archive for rational mechanics and analysis,1976,63(4):337-403.
[11]CIARLET P G. Mathematical elasticity. Mathematics and its applications[M]. Amsterdan:North-Holland Publishing Company,1988:199-265.
[12]YANG X D,DIAO Z G,LIU S H. Some inequalities for sum of Hermitian matrices[J]. Mathematica appllcate,2015,28(3):475-480.
[13]王伯英,张福振. 矩阵乘积的特征值和奇异值的不等式[J]. 北京师范大学学报(自然科学版),1987(3):1-4.
[14]陈道琦. 关于半正定Hermite矩阵乘积迹的一个不等式[J]. 数学学报,1988,31(2):565-569.
[15]WANG B Y,XI B Y,ZHANG F. Some inequalities for sum and product of positive semidefinite matrices[J]. Linear algebra and its applications,1999,293(1):39-49.

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备注/Memo

备注/Memo:
收稿日期:2017-03-16.
基金项目:国家自然科学青年基金(11501300)、江苏省青年科学基金(BK20130985).
通讯联系人:杨兴东,教授,研究方向:数值代数. E-mail:xdyangnuist@163.com
更新日期/Last Update: 2018-03-31