Inverse eigenvalue problem for Euclidean distance matrices of Size 3

Authors

  • Jolanda Modic FMF, University of Ljubljana, Slovenia XLAB, d.o.o., Ljubljana, Slovenia
  • GaÅ¡per Jaklič FMF and IMFM, University of Ljubljana, Slovenia and IAM, University of Primorska, Ljubljana, Slovenia,

Keywords:

Euclidean distance matrix, inverse eigenvalue problem, bordered matrix

Abstract

A matrix is Euclidean distance matrix (EDM) if there exist points such that the matrix elements are squares of distances between the corresponding points. The inverse eigenvalue problem (IEP) is as follows: construct (or prove the existence of) a matrix with particular properties and a given spectrum. It is well known that the inverse eigenvalue problem for Euclidean distance matrices of size 3 has a solution. In this paper all solutions of the problem are given and their relation with geometry is studied. Possible extension to larger EDMs is tackled. DOI: 10.1017/S0004972712000755

Published

2012-12-17

Issue

Vol. 87 No. 1 (2013)

Section

Articles
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