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.
Acknowledgements
Research supported by the Natural Sciences and Engineering Research Council of Canada and MITACS.
Notes
1 Some authors refer to these as EDMs of strength one Citation6.