Compatible preorders and linear operators on \({\mathbb{R}}^ n\)
type: Item
instance of: scholarly article
title: Compatible preorders and linear operators on \({\mathbb{R}}^ n\)
zbMATH Open document ID: 0726.15014
DOI: 10.1016/0024-3795(91)90209-F
author: Ivan Singer
author: Juan-Enrique Martínez-Legaz
published in: Linear Algebra and its Applications
publication date: 1991-01-01T00:00:00Z
review text: The authors characterize preorders (quasiorders, reflexive transitive binary relations) $R$-compatible with the vector space structure on \(R^ n\) in the sense that, if \(xRy\), \(zRw\), then \((x+z)R(y+w)\) and \((cx)R(cy)\), $c$ positive, and studies representations as intersections of total orders of the same type.
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 06F20
zbMATH DE Number: 4198209
zbMATH Keywords: linear operators
zbMATH Keywords: compatible preorder
zbMATH Keywords: ordered group
zbMATH Keywords: Szpilrajn theorem
zbMATH Keywords: preordered vector space
zbMATH Keywords: quasiorders
zbMATH Keywords: total orders
reviewed by: Ki Hang Kim
MaRDI profile type: Publication
cites work: Q3964625
cites work: Q5657176
cites work: Q5527606
cites work: Q3685582
cites work: Exact quasiconvex conjugation
cites work: Q3677521
cites work: Lexicographical separation in \({\mathbb{R}}^ n\)
cites work: Surrogate duality for vector optimization
cites work: The structure of hemispaces in \({\mathbb{R}}^ n\)
cites work: Lexicographical order, lexicographical index, and linear operators
cites work: Q5555984
cites work: Q3343218
description: scientific article; zbMATH DE number 4198209