On faces generated by certain positive linear transformations
type: Item
instance of: scholarly article
title: On faces generated by certain positive linear transformations
zbMATH Open document ID: 0679.15016
DOI: 10.1016/0024-3795(89)90575-2
author: Raphael Loewy
published in: Linear Algebra and its Applications
publication date: 1989-01-01T00:00:00Z
review text: The paper deals with the cone of \(m\times n\) real matrices mapping a cone \(K_ 1\) in \({\mathbb{R}}^ n\) into a cone \(K_ 2\) in \({\mathbb{R}}^ m\). In the first part of the paper it is assumed that the matrices are of fixed rank and map the extreme rays of \(K_ 1\) into extreme rays of \(K_ 2\). Then under further assumptions an upper bound for the dimension of the face generated in the mapping cone of each of these matrices is given. In the second part of the paper it is shown that if a non-singular matrix maps the exposed rays of an indecomposable cone into itself then the matrix determines an exposed ray in the mapping cone.
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 47L07
zbMATH DE Number: 4112783
zbMATH Keywords: cone of real matrices
zbMATH Keywords: extreme rays
zbMATH Keywords: exposed rays
zbMATH Keywords: indecomposable cone
reviewed by: Tage Bai Andersen
MaRDI profile type: Publication
full work available at URL: 0024-3795(89)90575-2
OpenAlex ID: W1996701468
cites work: The lattice of faces of a finite dimensional cone
cites work: Theory of cones
cites work: Extreme operators on polyhedral cones
cites work: Dimension of faces generated by certain positive linear operators
cites work: Indecomposable cones
cites work: Positive operators on the \(n\)-dimensional ice cream cone
cites work: State Constraints in Convex Control Problems of Bolza
cites work: Cross-Positive Matrices
description: scientific article; zbMATH DE number 4112783