Email this article Combinatorial and Spectral Properties of Semigroups of Stochastic Matrices
- Authors: Al’pin Y.A.1, Al’pina V.S.2
-
Affiliations:
- Kazan’ Federal University
- Kazan’ National Research Technological University
- Issue: Vol 216, No 6 (2016)
- Pages: 730-737
- Section: Article
- URL: https://bakhtiniada.ru/1072-3374/article/view/237914
- DOI: https://doi.org/10.1007/s10958-016-2936-5
- ID: 237914
Cite item
Open Access
Access granted
Subscription Access
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 stochastic matrices and the spectral properties of matrices in the semigroup is presented.
About the authors
Yu. A. Al’pin
Kazan’ Federal University
Author for correspondence.
Email: Yuri.Alpin@ksu.ru
Russian Federation, Kazan’
V. S. Al’pina
Kazan’ National Research Technological University
Email: Yuri.Alpin@ksu.ru
Russian Federation, Kazan’
Supplementary files
