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Multispherical Euclidean distance matrices

โœ Scribed by Hiroshi Kurata; Pablo Tarazaga

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
178 KB
Volume
433
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

In this paper we introduce new necessary and sufficient conditions for an Euclidean distance matrix to be multispherical. The class of multispherical distance matrices studied in this paper contains not only most of the matrices studied by Hayden et al. (1996) [2], but also many other multispherical structures that do not satisfy the conditions in Hayden et al. (1996) [2]. We also study the information provided by the origin of coordinates when it is placed at the center of the spheres and the origin representation property is satisfied. These vectors associated with the origin of coordinates generate a number of supporting hyperplanes for a family of multispherical matrices and also describe part of the null space of the corresponding distance matrices.

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