Vol. 12, No. 7, 2019

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Sign pattern matrices that allow inertia $\mathbb{S}_{n}$

Adam H. Berliner, Derek DeBlieck and Deepak Shah

Vol. 12 (2019), No. 7, 1229–1240
Abstract

Sign pattern matrices of order n that allow inertias in the set Sn are considered. All sign patterns of order 3 (up to equivalence) that allow S3 are classified and organized according to their associated directed graphs. Furthermore, a minimal set of such matrices is found. Then, given a pattern of order n that allows Sn, a construction is given that generates families of irreducible sign patterns of order n + 1 that allow Sn+1.

Keywords
sign pattern, zero-nonzero pattern, inertia, digraph, Jacobian
Mathematical Subject Classification 2010
Primary: 15B35, 15A18, 05C50
Secondary: 05C20
Milestones
Received: 29 January 2019
Revised: 8 June 2019
Accepted: 22 June 2019
Published: 12 October 2019

Communicated by Chi-Kwong Li
Authors
Adam H. Berliner
Department of Mathematics, Statistics, and Computer Science
St. Olaf College
Northfield, MN
United States
Derek DeBlieck
St. Olaf College
Northfield, MN
United States
Deepak Shah
St. Olaf College
Northfield, MN
United States