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AN EIGENVALUE CHARACTERISATION OF THE DUAL EDM CONE

Part of: Basic linear algebra Special matrices

Published online by Cambridge University Press:  18 November 2021

KYLE BRODER Open the ORCID record for KYLE BRODER [Opens in a new window]
KYLE BRODER*
Affiliation:
Mathematical Sciences Institute, Australian National University, Acton, ACT 2601, Australia and BICMR, Peking University, Beijing 100871, PR China
*
e-mail: [email protected]
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Abstract

We show that the elements of the dual of the Euclidean distance matrix cone can be described via an inequality on a certain weighted sum of its eigenvalues.

Keywords

Euclidean distance matricesEDM conedual EDM coneeigenvaluesweighted graphsDirichlet energy of weighted graphs

MSC classification

Primary: 15A18: Eigenvalues, singular values, and eigenvectors
Secondary: 15B48: Positive matrices and their generalizations; cones of matrices 15B57: Hermitian, skew-Hermitian, and related matrices
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 106 , Issue 1 , August 2022 , pp. 67 - 69
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

Supported by an Australian Government Research Training Program (RTP) Scholarship.

References

Broder, K., ‘On the nonnegativity of the Dirichlet energy of a weightedgraph’, Bull. Aust. Math. Soc., to appear.Google Scholar
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Schoenberg, I. J., ‘Remarks to Maurice Fréchet’s article“Sur la définition axiomatique d’une classe déspace distanciés vectoriellement applicable sur l’espace deHilbert”’, Ann. of Math. (2) 36(3) (1935),724–732.CrossRefGoogle Scholar