A note on the spectra of certain skew-symmetric \(\{1,0,-1\}\)-matrices
type: Item
instance of: scholarly article
title: A note on the spectra of certain skew-symmetric \(\{1,0,-1\}\)-matrices
zbMATH Open document ID: 1008.05094
DOI: 10.1016/S0012-365X(02)00402-8
author: Gerhard Wesp
published in: Discrete Mathematics
publication date: 2002-12-02T00:00:00Z
review text: The author gives equivalent characterizations of skew-symmetric \(\{1,0,-1\}\) matrices \(A=(a_{xy})\) satisfying the property \(a_{wx}a_{yz}+ a_{wy}a_{zx}+ a_{wz}a_{xy}= a_{wx}a_{wy}a_{wz}a_{xy}a_{xz}a_{yz}\) for all distinct \(x,y,z,w\) in \(\{1,2,\dots,n\}\) related to the Pfaffian of \(A\). As an implication, the author is able to characterize the unimodular orientations of the complete graph, chirotopes of rank 2, and of a class of multipartite oriented graphs.
reviewed by: Dragan Stevanović
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 52C40
zbMATH DE Number: 1839040
zbMATH Keywords: Pfaffian form
zbMATH Keywords: skew-symmetric matrix
zbMATH Keywords: eigenvalue
zbMATH Keywords: chirotope
zbMATH Keywords: oriented graphs
zbMATH Keywords: unimodular matrix
MaRDI profile type: Publication
full work available at URL: s0012-365x(02)00402-8
OpenAlex ID: W1966783337
description: scientific article; zbMATH DE number 1839040