Some necessary and some sufficient trace inequalities for Euclidean distance matrices

Authors: Alfakih, A. Y.¹; Wolkowicz, Henry²

Source: Linear and Multilinear Algebra, Volume 55, Number 5, September 2007 , pp. 499-506(8)

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Abstract:

In this article, we use known bounds on the smallest eigenvalue of a symmetric matrix and Schoenberg's theorem to provide both necessary as well as sufficient trace inequalities that guarantee a matrix D is a Euclidean distance matrix, EDM. We also provide necessary and sufficient trace inequalities that guarantee a matrix D is an EDM generated by a regular figure.

Keywords: Euclidean distance matrices; Smallest eigenvalue; AMS Subject Classifications; 15A45; 15A57

Document Type: Research article

DOI: http://dx.doi.org/10.1080/03081080701241570

Affiliations: 1: Department of Mathematics and Statistics, University of Windsor, Ontario, Canada 2: University of Waterloo, Department of Combinatorics and Optimization, Waterloo, Ontario N2L 3G1, Canada

Publication date: 2007-09-01