# Eutactic star closest to a given star

## Abstract

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.

- Authors:

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

- Publication Date:

- OSTI Identifier:
- 20929719

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 5; Other Information: DOI: 10.1063/1.2734863; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; ALGORITHMS; CRYSTALLOGRAPHY; DECOMPOSITION; GRAPH THEORY; HILBERT SPACE; MATRICES

### Citation Formats

```
Gomez, A., Torres, M., Aragon, J. L., Instituto de Fisica Aplicada, Consejo Superior de Investigaciones Cientificas, Serrano 144, 28006 Madrid, and Centro de Fisica Aplicada y Tecnologia Avanzada, Universidad Nacional Autonoma de Mexico, Apartado Postal 1-1010, Queretaro 76000.
```*Eutactic star closest to a given star*. United States: N. p., 2007.
Web. doi:10.1063/1.2734863.

```
Gomez, A., Torres, M., Aragon, J. L., Instituto de Fisica Aplicada, Consejo Superior de Investigaciones Cientificas, Serrano 144, 28006 Madrid, & Centro de Fisica Aplicada y Tecnologia Avanzada, Universidad Nacional Autonoma de Mexico, Apartado Postal 1-1010, Queretaro 76000.
```*Eutactic star closest to a given star*. United States. doi:10.1063/1.2734863.

```
Gomez, A., Torres, M., Aragon, J. L., Instituto de Fisica Aplicada, Consejo Superior de Investigaciones Cientificas, Serrano 144, 28006 Madrid, and Centro de Fisica Aplicada y Tecnologia Avanzada, Universidad Nacional Autonoma de Mexico, Apartado Postal 1-1010, Queretaro 76000. Tue .
"Eutactic star closest to a given star". United States.
doi:10.1063/1.2734863.
```

```
@article{osti_20929719,
```

title = {Eutactic star closest to a given star},

author = {Gomez, A. and Torres, M. and Aragon, J. L. and Instituto de Fisica Aplicada, Consejo Superior de Investigaciones Cientificas, Serrano 144, 28006 Madrid and Centro de Fisica Aplicada y Tecnologia Avanzada, Universidad Nacional Autonoma de Mexico, Apartado Postal 1-1010, Queretaro 76000},

abstractNote = {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.},

doi = {10.1063/1.2734863},

journal = {Journal of Mathematical Physics},

number = 5,

volume = 48,

place = {United States},

year = {Tue May 15 00:00:00 EDT 2007},

month = {Tue May 15 00:00:00 EDT 2007}

}

DOI: 10.1063/1.2734863

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