Bases in max-algebra

Raymond Cuninghame-Green, Peter Butkovic

Research output: Contribution to journalArticle

44 Citations (Scopus)


For n-tuples over the algebraic system (R, circle plus, circle times) = (R, max, +), concepts such as linear dependence, space and basis may be defined by analogy with classical linear algebra. Whenever a space is finitely generated, it possesses a basis and all its bases are trivially related and therefore have the same cardinality. However, for any given n > 2, spaces with bases of arbitrary cardinality may be constructed, as well as spaces with no basis. (C) 2004 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)107-120
Number of pages14
JournalLinear Algebra and its Applications
Publication statusPublished - 1 Jan 2004


  • generating set
  • basis
  • max-algebra
  • independent set


Dive into the research topics of 'Bases in max-algebra'. Together they form a unique fingerprint.

Cite this