An inequality for the distances between finitely many points on a hypersphere
type: Item
instance of: scholarly article
title: An inequality for the distances between finitely many points on a hypersphere
zbMATH Open document ID: 0684.51014
author: Jianong Zhou
published in: Chinese Science Bulletin
publication date: 1989-01-01T00:00:00Z
review text: The author discusses squared distance matrices in \(E^ n\). He obtains an inequality for the distances between a finite point set on a hypersphere, containing their squared distances and a constant which depends only on the dimension. It becomes an equality iff all the negative eigenvalues of the squared distance matrix A of the point set are equal. The proof uses assertions about the eigenvalues of A. Then he gives corollaries for special point sets on a hypersphere and for geodesic distances of a point set in a spherical space.
Mathematics Subject Classification ID: 51K99
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 51M10
zbMATH DE Number: 4120894
zbMATH Keywords: inequality
zbMATH Keywords: hypersphere
zbMATH Keywords: distance matrix
zbMATH Keywords: geodesic distances
reviewed by: Johannes Böhm
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4120894