Z-Pencils
Rings and Algebras
2007-05-23 v1 Combinatorics
Abstract
The matrix pencil (A,B) = {tB-A | t \in C} is considered under the assumptions that A is entrywise nonnegative and B-A is a nonsingular M-matrix. As t varies in [0,1], the Z-matrices tB-A are partitioned into the sets L_s introduced by Fiedler and Markham. As no combinatorial structure of B is assumed here, this partition generalizes some of their work where B=I. Based on the union of the directed graphs of A and B, the combinatorial structure of nonnegative eigenvectors associated with the largest eigenvalue of (A,B) in [0,1) is considered.
Keywords
Cite
@article{arxiv.math/9807026,
title = {Z-Pencils},
author = {J. J. McDonald and D. D. Olesky and H. Schneider and M. J. Tsatsomeros and P. van den Driessche},
journal= {arXiv preprint arXiv:math/9807026},
year = {2007}
}
Comments
8 pages, LaTex