Bases in max-algebra
type: Item
instance of: scholarly article
title: Bases in max-algebra
zbMATH Open document ID: 1059.15001
published in: Linear Algebra and its Applications
publication date: 2004-11-22T00:00:00Z
review text: The authors consider bases for spaces of vectors over the semiring \((\mathbb R, \max, +)\). It is proved that all bases for a subset have the same cardinality; there exist subsets of \(\mathbb R^n\) having bases of arbitrary cardinality iff \(n\geq 3\); subsets have (finite) bases iff they are finitely generated, that \(\mathbb R^n\), \(n>1\) has no basis in this sense, and if bases were allowed to be infinite, under certain conditions bases would still not exist. One special feature of the definition is that in writing \(w\) as a linear combination of some set \(U\) of vectors, the linear combination is not allowed to involve \(w\) itself.
Mathematics Subject Classification ID: 15A80
Mathematics Subject Classification ID: 15A03
zbMATH DE Number: 2117285
zbMATH Keywords: max-algebra
zbMATH Keywords: independent set
zbMATH Keywords: generating set
zbMATH Keywords: basis
zbMATH Keywords: semiring
author: R. A. Cuninghame-Green
author: Peter Butkovič
reviewed by: Ki Hang Kim
MaRDI profile type: Publication
full work available at URL: j.laa.2004.03.022
OpenAlex ID: W2070098696
cites work: Q4304869
cites work: An Algebra for Network Routing Problems
cites work: Minimax algebra
cites work: Q3684177
cites work: Moduloïds and pseudomodules. I: Dimension theory
cites work: Linear and combinatorial optimization in ordered algebraic structures
DOI: 10.1016/J.LAA.2004.03.022
description: scientific article; zbMATH DE number 2117285