X-simple image eigencones of tropical matrices

Jan Plavka, Sergey Sergeev

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
127 Downloads (Pure)


We investigate max-algebraic (tropical) one-sided systems A⊗x=b where b is an eigenvector and x lies in an interval X. A matrix A is said to have X-simple image eigencone associated with an eigenvalue λ, if any eigenvector x associated with λ and belonging to the interval X is the unique solution of the system A⊗y=λx in X. We characterize matrices with X-simple image eigencone geometrically and combinatorially, and for some special cases, derive criteria that can be efficiently checked in practice.
Original languageEnglish
Pages (from-to)169-190
JournalLinear Algebra and its Applications
Early online date8 Jun 2016
Publication statusPublished - 15 Oct 2016


  • Max algebra
  • one-sided system
  • weakly robust
  • interval analysis


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