Completely positive factorizations associated with Euclidean distance matrices corresponding to an arithmetic progression
Spectral Theory
2023-08-09 v1
Abstract
Euclidean distance matrices corresponding to an arithmetic progression have rich spectral and structural properties. We exploit those properties to develop completely positive factorizations of translations of those matrices. We show that the minimal translation that makes such a matrix positive semidefinite results in a completely positive matrix. We also discuss completely positive factorizations of such matrices over the integers. Methods developed in the paper can be used to find completely positive factorizations of other matrices with similar properties.
Cite
@article{arxiv.1909.12649,
title = {Completely positive factorizations associated with Euclidean distance matrices corresponding to an arithmetic progression},
author = {Damjana Kokol Bukovšek and Thomas Laffey and Helena Šmigoc},
journal= {arXiv preprint arXiv:1909.12649},
year = {2023}
}