THE GOLDEN-THOMPSON TRACE INEQUALITY IS COMPLEMENTED

被引：87

作者：

HIAI, F ^{[1
]}

PETZ, D ^{[1
]}

机构：

[1] HUNGARIAN ACAD SCI,INST MATH,H-1364 BUDAPEST,HUNGARY

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 1993年 / 181卷

关键词：

D O I：

10.1016/0024-3795(93)90029-N

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a class of trace inequalities which complements the Golden-Thompson inequality. For example, Tr(e(pA) # e(pB))2/p less-than-or-equal-to Tr e(A+B) holds for all p > 0 when A and B are Hermitian matrices and # denotes the geometric mean. We also prove related trace inequalities involving the logarithmic function; namely p-1 Tr X log Y(p)/2X(p)Y(p)/2) less-than-or-equal-to Tr X(log X + log Y) less-than-or-equal-to p-1 Tr X log X(p)/2Y(p)X(p)/2 for all p > 0 when X and Y are nonnegative matrices. These inequalities supply lower and upper bounds on the relative entropy.

引用

页码：153 / 185

页数：33

共 34 条

[1] MAJORIZATION, DOUBLY STOCHASTIC MATRICES, AND COMPARISON OF EIGENVALUES [J].