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This article is cited in 2 scientific papers (total in 2 papers)
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
$A_1,\dots,A_n\in\mathcal A$ 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.
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
Linking options:
https://www.mathnet.ru/eng/dm394https://doi.org/10.4213/dm394 https://www.mathnet.ru/eng/dm/v11/i4/p79
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Abstract page: | 405 | Full-text PDF : | 256 | First page: | 1 |
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