Zero forcing for sign patterns

TL;DR

The paper introduces signed zero forcing, a new variant of zero forcing, to bound the maximum nullity of matrices with specific sign patterns, extending classical methods to sign-constrained matrices.

Contribution

It develops signed zero forcing as a novel tool to analyze maximum nullity for sign patterns, generalizing classical zero forcing techniques.

Findings

Provides bounds for nullity of Z-matrices with line graph structure

Extends zero forcing concepts to sign patterns

Enables computation of maximum nullity in new matrix classes

Abstract

We introduce a new variant of zero forcing - signed zero forcing. The classical zero forcing number provides an upper bound on the maximum nullity of a matrix with a given graph (i.e. zero-nonzero pattern). Our new variant provides an analo- gous bound for the maximum nullity of a matrix with a given sign pattern. This allows us to compute, for instance, the maximum nullity of a Z-matrix whose graph is L(K_{n}), the line graph of a clique.