Eutactic star closest to a given star

Journal Article · Tue May 15 00:00:00 EDT 2007 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2734863· OSTI ID:20929719

Gomez, A; Torres, M; Aragon, J L ^[1]

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1. Departamento de Materia Condensada, Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Mexico D.F. C.P. 04510 (Mexico)

A eutactic star is a set of M vectors in R{sup n} (M>n) that are projections of M orthogonal vectors in R{sup M}. Eutactic stars have remarkable properties that have been exploited in several fields such as crystallography, graph theory, wavelets, and quantum measurement theory. In this work we show that given an arbitrary star of vectors, there exists a closest eutactic star in the Frobenius norm. An algorithm for calculating this star is presented. Additionally, the distance between both stars provides a new measure of eutacticity.

• OSTI ID: 20929719
• Journal Information: Journal of Mathematical Physics, Vol. 48, Issue 5; Other Information: DOI: 10.1063/1.2734863; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
ALGORITHMS
CRYSTALLOGRAPHY
DECOMPOSITION
GRAPH THEORY
HILBERT SPACE
MATRICES