The number of negative entries in a sign pattern allowing orthogonality
type: Item
instance of: scholarly article
title: The number of negative entries in a sign pattern allowing orthogonality
zbMATH Open document ID: 1063.15022
author: Yanling Shao
author: Yubin Gao
published in: Graphs and Combinatorics
publication date: 2005-01-20T00:00:00Z
review text: The authors show that the following result holds for all \(n\geq 3\). Among the \(n\times n\) real orthogonal matrices without zero entries, the number of negative entries can take any integer value in the interval \([n-1,n^2-n+1]\). Values outside that interval clearly cannot be achieved since they would require the matrix to have two columns in which all entries have the same sign, and such columns cannot be orthogonal.
reviewed by: Ian M. Wanless
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 2130302
zbMATH Keywords: sign pattern
zbMATH Keywords: \(\pm\) sign
zbMATH Keywords: qualitative class
zbMATH Keywords: orthogonal matrix
MaRDI profile type: Publication
full work available at URL: s00373-004-0575-y
OpenAlex ID: W2047382183
DOI: 10.1007/S00373-004-0575-Y
description: scientific article; zbMATH DE number 2130302