On some matrix inequalities

被引：22

作者：

Zhan, XZ ^{[1
]}

机构：

[1] E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2004年 / 376卷

关键词：

singular value; norm; trace inequalities;

D O I：

10.1016/j.laa.2003.08.008

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*) less than or equal to s(j)(A*A + B*B), j = 1, 2,... for any matrices A, B. We first give new proofs of this inequality and its equivalent form. Then we use it to prove the following trace inequality: let A(0) be a positive definite matrix and A(1),...,A(k) be positive semidefinite matrices. Then tr Sigma(j=1)(k) (Sigma(i=0)(j)A(i))(-2)A(j) < tr A(0)(-1). (C) 2003 Elsevier Inc. All rights reserved.

引用

页码：299 / 303

页数：5

共 8 条

[1] AN INEQUALITY FOR A SUM OF QUADRATIC-FORMS WITH APPLICATIONS TO PROBABILITY-THEORY [J].

ANDERSON, TW ;

TAYLOR, JB .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1980, 30 (APR) :93-99

[2] 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

[3]

BHATIA R., 1997, GTM, V169

[4] Singular values of compressions, restrictions and dilations [J].

Bourin, JC .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2003, 360 :259-272

[5] Commutator inequalities associated with the polar decomposition [J].

Kittaneh, F .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 130 (05) :1279-1283

[6] Norm inequalities for certain operator sums [J].

Kittaneh, F .

JOURNAL OF FUNCTIONAL ANALYSIS, 1997, 143 (02) :337-348

[7]

ZHAN X, 2002, LNM, V1790

[8]

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

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