The Golden-Thompson trace inequality is complemented

Fumio Hiai, D. Petz

Research output: Contribution to journalArticle

67 Citations (Scopus)

Abstract

We prove a class of trace inequalities which complements the Golden-Thompson inequality. For example, Tr(epA#epB) 2 p≤Tr eA+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-1TrX log Y p> 2XpY p 2≤Tr X(log X+log Y)≤p-1TrX log X p 2YpX p 2 for all p>0 when X and Y are nonnegative matrices. These inequalities supply lower and upper bounds on the relative entropy.

Original languageEnglish
Pages (from-to)153-185
Number of pages33
JournalLinear Algebra and Its Applications
Volume181
Issue numberC
DOIs
Publication statusPublished - Mar 1 1993

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Trace Inequality
Geometric mean
Relative Entropy
Nonnegative Matrices
Hermitian matrix
Upper and Lower Bounds
Logarithmic
Entropy
Complement
Denote
Class

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis

Cite this

The Golden-Thompson trace inequality is complemented. / Hiai, Fumio; Petz, D.

In: Linear Algebra and Its Applications, Vol. 181, No. C, 01.03.1993, p. 153-185.

Research output: Contribution to journalArticle

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