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Diskr. Mat., 1999, Volume 11, Issue 4, Pages 79–88 (Mi dm394)  

This article is cited in 1 scientific paper (total in 1 paper)

An estimate for the exponent of some sets of nonnegative matrices

D. E. Efimov


Abstract: The exponent of a set $\mathcal A$ of non-negative $k\times k$ matrices is a minimal $n$ such that for any sample with replacement $A_1,…,A_n\in\mathcal A$ all elements of the matrix $A_1\ldots A_n$ are positive. We obtain upper bounds of the exponent of some sets of matrices with the use of singular values of matrices. We also give an estimate of the exponent of a set of matrices obtained with the use of a generalized Kronecker product of matrices. These results are used for estimating the length of the covering of a group by a given set of generators.

DOI: https://doi.org/10.4213/dm394

Full text: PDF file (748 kB)

English version:
Discrete Mathematics and Applications, 1999, 9:6, 653–663

Bibliographic databases:

UDC: 519.12
Received: 24.08.1998

Citation: D. E. Efimov, “An estimate for the exponent of some sets of nonnegative matrices”, Diskr. Mat., 11:4 (1999), 79–88; Discrete Math. Appl., 9:6 (1999), 653–663

Citation in format AMSBIB
\Bibitem{Efi99}
\by D.~E.~Efimov
\paper An estimate for the exponent of some sets of nonnegative matrices
\jour Diskr. Mat.
\yr 1999
\vol 11
\issue 4
\pages 79--88
\mathnet{http://mi.mathnet.ru/dm394}
\crossref{https://doi.org/10.4213/dm394}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1761014}
\zmath{https://zbmath.org/?q=an:0965.15025}
\transl
\jour Discrete Math. Appl.
\yr 1999
\vol 9
\issue 6
\pages 653--663


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. E. Efimov, “Estimation of the distance between partial products of some sequences of linear operators”, Discrete Math. Appl., 22:4 (2012), 427–434  mathnet  crossref  crossref  mathscinet  elib
  • Дискретная математика
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