ABSTRACT

A.1 Frobenius-Perron theorems (T1) Theorem 1. If A is non-negative and indecomposable there exists an α, x, and p such that:

(i) Ax= αx, with α > 0 and x> 0, and pA= αp, with p> 0

(ii) α is unique, and x and p are unique up to a multiplicative constant.