More results on singular value inequalities of matrices

被引：55

作者：

Tao, Yunxing ^{[1
]}

机构：

[1] Acad Armoured Forces Engn, Dept Fundamental Sci, Div Math, Beijing 100072, Peoples R China

[2] Beijing Normal Univ, Sch Math, Beijing 100875, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2006年 / 416卷 / 2-3期

关键词：

singular value; arithmetic-geometric mean; positive semidefinite matrix;

D O I：

10.1016/j.laa.2005.12.017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The arithmetic-geometric mean inequality for singular values due to Bhatia and Kittaneh says that 2s(j) (AB*) <= sj (A*A + B*B), j = 1, 2.... for any matrices A, B. We give a new equivalent form and some relevant generalizations of this inequality. In particular, we show that s(j) (A(1/4)B(3/4) +A(3/4) B-1/4) <= s(j)(A+B), j = 1,...,n for any n x n positive semidefinite matrices A, B, which proves a special case of Zhan's conjecture posed in 2000. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：724 / 729

页数：6

共 8 条

[1] ON THE SINGULAR-VALUES OF A PRODUCT OF OPERATORS [J].

BHATIA, R ;

KITTANEH, F .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1990, 11 (02) :272-277

[2] Notes on matrix arithmetic-geometric mean inequalities [J].

Bhatia, R ;

Kittaneh, F .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2000, 308 (1-3) :203-211

[3]

Bhatia R., 1997, GTM169

[4] Inequalities for sums and products of operators [J].

Hirzallah, O .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 407 :32-42

[5]

ZHAN X, 2002, LNM1790

[6] Some research problems on the Hadamard product and singular values of matrices [J].

Zhan, XZ .

LINEAR & MULTILINEAR ALGEBRA, 2000, 47 (02) :191-194

[7] On some matrix inequalities [J].

Zhan, XZ .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 376 :299-303

[8]

Zhan XZ, 2000, SIAM J MATRIX ANAL A, V22, P819, DOI 10.1137/S0895479800369840

← 1 →