Semigroups of Nonnegative Matrices

Part of the Universitext book series (UTX)


In this chapter we consider a stronger form of reducibility for collections of matrices with nonnegative entries, which we simply call nonnegative matrices. The results will also be applied to questions of ordinary reducibility. A substantial part of the chapter is devoted to extensions to semigroups of the Perron-Frobenius Theorem on the existence of positive eigenvectors for nonnegative matrices and symmetries of their spectra (Corollary 5.2.13 below).


Spectral Radius Diagonal Entry Nonnegative Matrix Permutation Matrice Nonnegative Matrice 
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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  1. 1.Department of MathematicsDalhousie UniversityHalifaxCanada
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada

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