Open Access
2019 Sign pattern matrices that allow inertia $\mathbb{S}_{n}$
Adam H. Berliner, Derek DeBlieck, Deepak Shah
Involve 12(7): 1229-1240 (2019). DOI: 10.2140/involve.2019.12.1229

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.

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Adam H. Berliner. Derek DeBlieck. Deepak Shah. "Sign pattern matrices that allow inertia $\mathbb{S}_{n}$." Involve 12 (7) 1229 - 1240, 2019. https://doi.org/10.2140/involve.2019.12.1229

Information

Received: 29 January 2019; Revised: 8 June 2019; Accepted: 22 June 2019; Published: 2019
First available in Project Euclid: 26 October 2019

zbMATH: 07140476
MathSciNet: MR4023349
Digital Object Identifier: 10.2140/involve.2019.12.1229

Subjects:
Primary: 05C50 , 15A18‎ , 15B35
Secondary: 05C20‎

Keywords: ‎digraph‎ , inertia , Jacobian , sign pattern , zero-nonzero pattern

Rights: Copyright © 2019 Mathematical Sciences Publishers

Vol.12 • No. 7 • 2019
MSP
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