Matrix convexity of functions of two variables
type: Item
instance of: scholarly article
title: Matrix convexity of functions of two variables
zbMATH Open document ID: 0805.15019
DOI: 10.1016/0024-3795(93)90119-9
author: Jaspal Singh Aujla
published in: Linear Algebra and its Applications
publication date: 1995-02-06T00:00:00Z
review text: It is shown that the separately matrix convex functions in two variables on a rectangle \(I \times J\) containing (0,0) are the functions satisfying the following inequality for all projections \(P\) and \(Q\) and all Hermitian matrices \(A\) and \(B\) with spectrum contained in \(I\) and \(J\) resp.: \[ (P \otimes Q) f(PAP,QBQ) (P \otimes Q) \leq (P \otimes Q) f(A,B) (P \otimes Q). \] It is also shown that the two notions matrix convexity on \(I \times I\) and diagonal matrix convexity on \(I \times I\) coincide.
reviewed by: Tage Bai Andersen
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 15A54
Mathematics Subject Classification ID: 26B25
zbMATH DE Number: 540062
zbMATH Keywords: matrix convex functions
zbMATH Keywords: inequality
zbMATH Keywords: Hermitian matrices
zbMATH Keywords: matrix convexity
MaRDI profile type: Publication
full work available at URL: 0024-3795(93)90119-9
OpenAlex ID: W2084836632
cites work: Q4169818
cites work: A Schwarz Inequality for Convex Operator Functions
cites work: Q5593024
cites work: Q4405419
cites work: Jensen's inequality for operators and Loewner's theorem
cites work: On Some Classes of Analytic Functions of Several Variables
cites work: Über monotone Matrixfunktionen
Wikidata QID: Q126808004
description: scientific article; zbMATH DE number 540062