A Perron-Frobenius-type Theorem for Positive Matrix Semigroups

Autor:	Heydar Radjavi, Gordon MacDonald, Leo Livshits
Rok vydání:	2016
Předmět:	Combinatorics Perron–Frobenius theorem Matrix (mathematics) Permutation Integer Semigroup General Mathematics Nonnegative matrix Type (model theory) Indecomposable module Analysis Theoretical Computer Science Mathematics
Zdroj:	Positivity. 21:61-72
ISSN:	1572-9281 1385-1292
Popis:	One consequence of the Perron–Frobenius Theorem on indecomposable positive matrices is that whenever an $$n\times n$$ matrix A dominates a non-singular positive matrix, there is an integer k dividing n such that, after a permutation of basis, A is block-monomial with $$k\times k$$ blocks. Furthermore, for suitably large exponents, the nonzero blocks of $$A^m$$ are strictly positive. We present an extension of this result for indecomposable semigroups of positive matrices.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::76ad80ef8a05515587bdeb5285c0b22c https://doi.org/10.1007/s11117-016-0403-7 Zobrazit plný text záznamu Full text from SpringerLink