A Perron-Frobenius-type Theorem for Positive Matrix Semigroups

被引：0

作者：

Livshits, L. ^{[1
]}

MacDonald, G. ^{[2
]}

Radjavi, H. ^{[3
]}

机构：

[1] Colby Coll, Dept Math, Waterville, ME 04901 USA

[2] Univ Prince Edward Isl, Dept Math & Stat, Charlottetown, PE, Canada

[3] Univ Waterloo, Dept Pure Math, Waterloo, ON, Canada

来源：

POSITIVITY | 2017年 / 21卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Matrix; Semigroup; Positive; Indecomposable; Perron-Frobenius Theorem;

D O I：

10.1007/s11117-016-0403-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

One consequence of the Perron-Frobenius Theorem on indecomposable positive matrices is that whenever an 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 blocks. Furthermore, for suitably large exponents, the nonzero blocks of are strictly positive. We present an extension of this result for indecomposable semigroups of positive matrices.

引用

页码：61 / 72

页数：12