Z-Pencils

1998/07/06 by J. J. McDonald, D. D. Olesky, H. Schneider +2
Mathematics · #math.RA #math.CO #msc:15A22 #msc:15A48 #msc:05C50

paper · pdf

published as Electronic Linear Algebra, 4 : 32-38, 1998 · 8 pages, LaTex

arxiv created 1998/07/06 · arxiv updated 2009/11/30

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 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.

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