Yu. A. Al'pin, V. S. Al'pina, “Indices of imprimitivity of the temporal components of a semigroup of nonnegative matrices”, Zap. Nauchn. Sem. POMI, 2018, Volume 472,Pages <nobr>17

Indices of imprimitivity of the temporal components of a semigroup of nonnegative matrices

Yu. A. Al'pin^a, V. S. Al'pina^b

^a Kazan (Volga Region) Federal University, Kazan, Russia
^b Kazan National Research Technological University, Kazan, Russia

Abstract: It is proved that the index of imprimitivity of a semigroup of nonnegative block-monominal matrices free of zero rows decomposes into a sum of the indices of imprimitivity of its temporal components, and if the semigroup is block irreducible, then the indices of imprimitivity of all the temporal components are equal.

Key words and phrases: irreducible nonnegative matrix, Frobenius form, imprimitivity index.

UDC: 512.6

Received: 22.10.2018