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Zap. Nauchn. Sem. POMI, 2016, Volume 453, Pages 5–14 (Mi znsl6366)  

Locally strongly primitive semigroups of nonnegative matrices

Yu. A. Al'pina, V. S. Al'pinab

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

Abstract: The class of locally strongly primitive semigroups of nonnegative matrices is introduced. It is shown that, by a certain permutation similarity, all the matrices of a semigroup of the class considered can be brought to block monomial form; moreover, any matrix product of sufficient length has positive nonzero blocks only. This shows that the following known property of an imprimitive nonnegative matrix in Frobenius form is inherited. If such a matrix is raised to a sufficiently high power, then all its nonzero blocks are positive. A combinatorial criterion of the locally strong primitivity of a semigroup of nonnegative matrices is found.

Key words and phrases: Frobenius theorem, imprimitivity index, strong primitive semigroup of nonnegative matrices.

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English version:
Journal of Mathematical Sciences (New York), 2017, 224:6, 815–820

Bibliographic databases:

Document Type: Article
UDC: 512.6
Received: 10.10.2016

Citation: Yu. A. Al'pin, V. S. Al'pina, “Locally strongly primitive semigroups of nonnegative matrices”, Computational methods and algorithms. Part XXIX, Zap. Nauchn. Sem. POMI, 453, POMI, St. Petersburg, 2016, 5–14; J. Math. Sci. (N. Y.), 224:6 (2017), 815–820

Citation in format AMSBIB
\Bibitem{AlpAlp16}
\by Yu.~A.~Al'pin, V.~S.~Al'pina
\paper Locally strongly primitive semigroups of nonnegative matrices
\inbook Computational methods and algorithms. Part~XXIX
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 453
\pages 5--14
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6366}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3593975}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 224
\issue 6
\pages 815--820
\crossref{https://doi.org/10.1007/s10958-017-3451-z}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85021264567}


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