Geodesic
A note on generalized Perron complements of $Z$-matrices
The electronic journal of linear algebra, Tome 15 (2006), pp. 8-13.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 15A48
Keywords: nonnegative matrix, Z-matrix, perron complement, irreducibility 
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     title = {A note on generalized {Perron} complements of $Z$-matrices},
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Ren, Zhi-Gang; Huang, Ting-Zhu; Cheng, Xiao-Yu. A note on generalized Perron complements of $Z$-matrices. The electronic journal of linear algebra, Tome 15 (2006), pp. 8-13. http://geodesic.mathdoc.fr/item/ELA_2006__15__a26/