The tropical rank of a tropical matrix

Zur Izhakian, Louis Rowen

Research output: Contribution to journalArticlepeer-review

51 Scopus citations


In this article, we develop further the theory of matrices over the extended tropical semiring. We introduce the notion of tropical linear dependence, enabling us to define matrix rank in a sense that coincides with the notions of tropical nonsingularity and invertibility.

Original languageEnglish
Pages (from-to)3912-3927
Number of pages16
JournalCommunications in Algebra
Issue number11
StatePublished - Nov 2009
Externally publishedYes


  • Extended tropical semiring
  • Linear algebra
  • Linear dependence
  • Matrix algebra
  • Pseudo invertibility
  • Rank of matrices


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