Z-Pencils

McDonald, J. J.; Olesky, D. D.; Schneider, H.; Tsatsomeros, M. J.; Driessche, P. van den

Z-Pencils

Authors

Driessche, P. van den

Description

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.
8 pages, LaTex