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

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

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 

• http://mi.mathnet.ru/eng/dm394
• https://doi.org/10.4213/dm394
• http://mi.mathnet.ru/eng/dm/v11/i4/p79

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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
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