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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 439, Pages 13–25 (Mi znsl6196)  
This article is cited in 3 scientific papers (total in 3 papers)

Combinatorial and spectral properties of semigroups of stochastic 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
Full-text PDF (182 kB) Citations (3)
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Abstract: The paper studies the notion of imprimitivity index of a semigroup of nonnegative matrices, introduced by Protasov and Voynov. A new characterization of the imprimitivity index in terms of the scrambling rank of a nonnegative matrix is suggested. Based on this characterization, an independent combinatorial proof of the Protasov–Voynov theorem on the interrelation between the imprimitivity index of a semigroup of stohastic matrices and the spectral properties of matrices in the semigroup is presented.
Key words and phrases: Perron–Frobenius theorem, imprimitivity index, semigrup of nonnegative matrices, stohastic matrices.
Received: 09.11.2015
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 216, Issue 6, Pages 730–737
DOI: https://doi.org/10.1007/s10958-016-2936-5
Bibliographic databases:
Document Type: Article
UDC: 512.6
Language: Russian
Citation: Yu. A. Al'pin, V. S. Al'pina, “Combinatorial and spectral properties of semigroups of stochastic matrices”, Computational methods and algorithms. Part XXVIII, Zap. Nauchn. Sem. POMI, 439, POMI, St. Petersburg, 2015, 13–25; J. Math. Sci. (N. Y.), 216:6 (2016), 730–737
Citation in format AMSBIB
\Bibitem{AlpAlp15}
\by Yu.~A.~Al'pin, V.~S.~Al'pina
\paper Combinatorial and spectral properties of semigroups of stochastic matrices
\inbook Computational methods and algorithms. Part~XXVIII
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 439
\pages 13--25
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6196}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3502378}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 216
\issue 6
\pages 730--737
\crossref{https://doi.org/10.1007/s10958-016-2936-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84976334782}
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  • https://www.mathnet.ru/eng/znsl/v439/p13
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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