Trace-Inequalities and Matrix-Convex Functions

Trace-Inequalities and Matrix-Convex Functions

A real-valued continuous function f(t) on an interval (α,β) gives rise to a map X↦f(X) via functional calculus from the convex set of n×n Hermitian matrices all of whose eigenvalues belong to the interval. Since the subpace of Hermitian matrices is provide...

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Autor principal: Tsuyoshi Ando
Formato: article
Lenguaje:EN
Publicado: SpringerOpen 2010
Materias:
Applied mathematics. Quantitative methods
T57-57.97
Analysis
QA299.6-433
Acceso en línea:https://doaj.org/article/36903d6be51c438ba447b08ba0fdb894
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spelling oai:doaj.org-article:36903d6be51c438ba447b08ba0fdb8942021-12-02T11:18:55ZTrace-Inequalities and Matrix-Convex Functions10.1155/2010/2419081687-18201687-1812https://doaj.org/article/36903d6be51c438ba447b08ba0fdb8942010-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2010/241908https://doaj.org/toc/1687-1820https://doaj.org/toc/1687-1812A real-valued continuous function f(t) on an interval (α,β) gives rise to a map X↦f(X) via functional calculus from the convex set of n×n Hermitian matrices all of whose eigenvalues belong to the interval. Since the subpace of Hermitian matrices is provided with the order structure induced by the cone of positive semidefinite matrices, one can consider convexity of this map. We will characterize its convexity by the following trace-inequalities: Tr(f(B)−f(A))(C−B)≤Tr(f(C)−f(B))(B−A) for A≤B≤C. A related topic will be also discussed. Tsuyoshi AndoSpringerOpenarticleApplied mathematics. Quantitative methodsT57-57.97AnalysisQA299.6-433ENFixed Point Theory and Applications, Vol 2010 (2010)
institution DOAJ
collection DOAJ
language EN
topic Applied mathematics. Quantitative methods
T57-57.97
Analysis
QA299.6-433
spellingShingle Applied mathematics. Quantitative methods
T57-57.97
Analysis
QA299.6-433
Tsuyoshi Ando
Trace-Inequalities and Matrix-Convex Functions
description A real-valued continuous function f(t) on an interval (α,β) gives rise to a map X↦f(X) via functional calculus from the convex set of n×n Hermitian matrices all of whose eigenvalues belong to the interval. Since the subpace of Hermitian matrices is provided with the order structure induced by the cone of positive semidefinite matrices, one can consider convexity of this map. We will characterize its convexity by the following trace-inequalities: Tr(f(B)−f(A))(C−B)≤Tr(f(C)−f(B))(B−A) for A≤B≤C. A related topic will be also discussed.
format article
author Tsuyoshi Ando
author_facet Tsuyoshi Ando
author_sort Tsuyoshi Ando
title Trace-Inequalities and Matrix-Convex Functions
title_short Trace-Inequalities and Matrix-Convex Functions
title_full Trace-Inequalities and Matrix-Convex Functions
title_fullStr Trace-Inequalities and Matrix-Convex Functions
title_full_unstemmed Trace-Inequalities and Matrix-Convex Functions
title_sort trace-inequalities and matrix-convex functions
publisher SpringerOpen
publishDate 2010
url https://doaj.org/article/36903d6be51c438ba447b08ba0fdb894
work_keys_str_mv AT tsuyoshiando traceinequalitiesandmatrixconvexfunctions
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