Z-Pencils

Details Z-Pencils Z-Pencils

1998-07-06

arxiv.org/abs/math/9807026v1

Electronic Linear Algebra, 4 : 32-38, 1998

Mathematics

Rings and Algebras

8 pages, LaTex

Scientific paper

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.

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