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INVERSE EIGENVALUE PROBLEM FOR EUCLIDEAN DISTANCE MATRICES OF SIZE 3

Part of: Basic linear algebra

Published online by Cambridge University Press:  15 October 2012

GAŠPER JAKLIČ  and
JOLANDA MODIC
GAŠPER JAKLIČ
Affiliation:
FMF and IMFM, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia IAM, University of Primorska, Jadranska 19, 1000 Ljubljana, Slovenia (email: [email protected])
JOLANDA MODIC*
Affiliation:
FMF, University of Ljubljana and XLAB d.o.o., Pot za Brdom 100, 1000 Ljubljana, Slovenia (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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A matrix is a 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 IEP for EDMs of size 3 has a solution. In this paper all solutions of the problem are given and their relation with geometry is studied. A possible extension to larger EDMs is tackled.

Keywords

Euclidean distance matrixinverse eigenvalue problembordered matrix

MSC classification

Secondary: 15A18: Eigenvalues, singular values, and eigenvectors
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 1 , February 2013 , pp. 82 - 93
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

Footnotes

This research was funded in part by the European Union, European Social Fund, Operational Programme for Human Resources, Development for the Period 2007–2013.

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