Perron vectors of an irreducible nonnegative interval matrix

Abstract

As is well known, an irreducible nonnegative matrix possesses a uniquely determined Perron vector. As the main result of this article we give a description of the set of Perron vectors of all the matrices contained in an irreducible nonnegative interval matrix A. This result is then applied to show that there exists a subset A * of A parameterized by n parameters (instead of n 2 ones in the description of A) such that for each A∈ A there exists a matrix A′∈ A * having the same spectral radius and the same Perron vector as A.