Indices of Imprimitivity of the Temporal Components of a Semigroup of Nonnegative Matrices

Abstract

© 2019, Springer Science+Business Media, LLC, part of Springer Nature. It is proved that the index of imprimitivity of a semigroup of nonnegative block-monomial matrices free of zero rows decomposes into the sum of the indices of imprimitivity of its temporal components, and if the semigroup is block irreducible, then the indices of imprimitivity of all its temporal components coincide.