X-simple image eigencones of tropical matrices

Jan Plavka, Sergey Sergeev

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
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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
JournalLinear Algebra and its Applications
Early online date8 Jun 2016
Publication statusE-pub ahead of print - 8 Jun 2016


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


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