Determinants, permanents and some applications to statistical shape theory

Francisco J. Caro-Lopera, Graciela González-Farías, N. Balakrishnan

Resultado de la investigación: Contribución a una revistaArtículoInvestigaciónrevisión exhaustiva

Resumen

A formula for the determinant of a matrix in terms of powers of traces is presented. Then, some expansions for powers of determinants of positive definite matrices in terms of zonal polynomials are derived. By making use of these, the associated elliptical families of matrixvariate distributions are obtained and applied in the framework of statistical shape theory, through the determination of the central non-isotropic configuration density. Finally, a relationship between the determinant and the permanent of a matrix is obtained. © 2012 Elsevier Inc.
Idioma originalInglés estadounidense
Páginas (desde-hasta)29-39
Número de páginas11
PublicaciónJournal of Multivariate Analysis
DOI
EstadoPublicada - 1 ene 2013

Huella dactilar

Determinant
Zonal Polynomials
Positive definite matrix
Trace
Polynomials
Configuration
Relationships
Framework
Family

Citar esto

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abstract = "A formula for the determinant of a matrix in terms of powers of traces is presented. Then, some expansions for powers of determinants of positive definite matrices in terms of zonal polynomials are derived. By making use of these, the associated elliptical families of matrixvariate distributions are obtained and applied in the framework of statistical shape theory, through the determination of the central non-isotropic configuration density. Finally, a relationship between the determinant and the permanent of a matrix is obtained. {\circledC} 2012 Elsevier Inc.",
author = "Caro-Lopera, {Francisco J.} and Graciela Gonz{\'a}lez-Far{\'i}as and N. Balakrishnan",
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Determinants, permanents and some applications to statistical shape theory. / Caro-Lopera, Francisco J.; González-Farías, Graciela; Balakrishnan, N.

En: Journal of Multivariate Analysis, 01.01.2013, p. 29-39.

Resultado de la investigación: Contribución a una revistaArtículoInvestigaciónrevisión exhaustiva

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AU - González-Farías, Graciela

AU - Balakrishnan, N.

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N2 - A formula for the determinant of a matrix in terms of powers of traces is presented. Then, some expansions for powers of determinants of positive definite matrices in terms of zonal polynomials are derived. By making use of these, the associated elliptical families of matrixvariate distributions are obtained and applied in the framework of statistical shape theory, through the determination of the central non-isotropic configuration density. Finally, a relationship between the determinant and the permanent of a matrix is obtained. © 2012 Elsevier Inc.

AB - A formula for the determinant of a matrix in terms of powers of traces is presented. Then, some expansions for powers of determinants of positive definite matrices in terms of zonal polynomials are derived. By making use of these, the associated elliptical families of matrixvariate distributions are obtained and applied in the framework of statistical shape theory, through the determination of the central non-isotropic configuration density. Finally, a relationship between the determinant and the permanent of a matrix is obtained. © 2012 Elsevier Inc.

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JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

SN - 0047-259X

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