On complex power nonnegative matrices

Francesco Tudisco, Valerio Cardinali, Carmine Di Fiore

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Power nonnegative matrices are defined as complex matrices having at least one nonnegative integer power. We exploit the possibility of deriving a Perron–Frobenius-like theory for these matrices, obtaining three main results and drawing several consequences. We study, in particular, the relationships with the set of matrices having eventually nonnegative powers, the inverse of M-type matrices and the set of matrices whose columns (rows) sum up to one.
Original languageEnglish
Pages (from-to)449-468
Number of pages20
JournalLinear Algebra and its Applications
Publication statusPublished - 15 Apr 2015


  • nonnegative matrices
  • eventually nonnegative matrices
  • power nonnegative matrices
  • stochastic matrices
  • Perron–Frobenius theory

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