A note on generalized Perron complements of Z-matrices

Abstract

The concept of the Perron complement of a nonnegative and irreducible matrix was
introduced by Meyer in 1989 and it was used to construct an algorithm for computing the stationary
distribution vector for Markov chains. Here properties of the generalized Perron complement of an
n×n irreducible Z-matrix K are considered. First the result that the generalized Perron complements
of K are irreducible Z-matrices is shown, and other properties are presented.