Differentiable transformations preserving a cone preordering
type: Item
instance of: scholarly article
title: Differentiable transformations preserving a cone preordering
zbMATH Open document ID: 0868.26015
DOI: 10.1016/0024-3795(93)00229-S
author: M. Niezgoda
author: Zdzisław Otachel
published in: Linear Algebra and its Applications
publication date: 1995-07-03T00:00:00Z
review text: The paper is concerned with vector preorderings (e.g., majorization) and real functions that preserve them. Extending to vector-valued functions a result of \textit{A. W. Marshall}, \textit{D. W. Walkup} and \textit{R. J.-B. Wets} [Pac. J. Math. 23, 569-584 (1967; Zbl 0153.38502)], the authors give a necessary and sufficient condition (in terms of directional derivatives) for a differentiable transformation to be isotone with respect to cone preorderings. The result is applied to characterize monotone matrix functions \(A\mapsto A^p\) with integer \(p\geq 2\) and isotone differentiable transformations with respect to \(G\)-majorizations, \(G\) being a finite reflection subgroup of the orthogonal group acting on \(\mathbb{R}^n\).
reviewed by: Ioan Raşa
Mathematics Subject Classification ID: 26E25
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 769049
zbMATH Keywords: vector preorderings
zbMATH Keywords: majorization
zbMATH Keywords: vector-valued functions
zbMATH Keywords: directional derivatives
zbMATH Keywords: monotone matrix functions
MaRDI profile type: Publication
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Wikidata QID: Q126981834
description: scientific article; zbMATH DE number 769049