On visualization scaling, subeigenvectors and Kleene stars in max algebra

Sergey Sergeev, H Schneider, Peter Butkovic

Research output: Contribution to journalArticle

39 Citations (Scopus)


The purpose of this paper is to investigate the interplay arising between max algebra, convexity and scaling problems. The latter, which have been studied in nonnegative matrix theory, are strongly related to max algebra. One problem is that of strict visualization scaling, defined as, for a given nonnegative matrix A, a diagonal matrix X such that all elements of X-1 AX are less than or equal to the maximum cycle geometric mean of A, with strict inequality for the entries which do not fie on critical cycles. In this paper such scalings are described by means of the max algebraic subeigenvectors and Kleene stars of nonnegative matrices as well as by some concepts of convex geometry. (c) 2009 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)2395-2406
Number of pages12
JournalLinear Algebra and its Applications
Issue number12
Publication statusPublished - 1 Dec 2009


  • Subeigenvectors
  • Max algebra
  • Kleene star
  • Diagonal similarity
  • Convex cones
  • Tropical convexity
  • Matrix scaling


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