Z-Pencils
J. J. McDonald, D. D. Olesky, H. Schneider, M. J. Tsatsomeros, P. van den Driessche
Abstract
The matrix pencil (A,B) = tB-A | t ∈ 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 Ls 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.
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