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INVERSE EIGENVALUE PROBLEM FOR EUCLIDEAN DISTANCE MATRICES OF SIZE 3

  • GAŠPER JAKLIČ (a1) (a2) and JOLANDA MODIC (a3)
Abstract

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.

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Copyright
Corresponding author
For correspondence; e-mail: jolanda.modic@gmail.com
Footnotes
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This research was funded in part by the European Union, European Social Fund, Operational Programme for Human Resources, Development for the Period 2007–2013.

Footnotes
References
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[1]Balaji, R. and Bapat, R. B., ‘Block distance matrices’, Electron. J. Linear Algebra 16 (2007), 435443.
[2]Chu, M. T., ‘Constructing a Hermitian matrix from its diagonal entries and eigenvalues’, SIAM J. Matrix Anal. Appl. 16 (1995), 207217.
[3]Chu, M. T. and Golub, G. H., Inverse Eigenvalue Problems: Theory, Algorithms, and Applications (Oxford University Press, Oxford, 2005).
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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