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.