ELA, Volume 15, pp. 8-13, January 2006, abstract.

A Note on Generalized Perron Complements of 
Z-matrices

Zhi-Gang Ren, Ting-Zhu Huang, and Xiao-Yu Cheng

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-by-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.