Determinants, permanents and some applications to statistical shape theorey

JOURNAL OF MULTIVARIATE ANALYSIS

卷:114

Article

Caro-Lopera, Francisco J.²  Gonzalez-Farias, Graciela¹  Balakrishnan, N.³ 

[1] Ctr Invest Matemat, Monterrey, Mexico

[2] Univ Medellin, Dept Ciencias Basicas, Medellin, Colombia

[3] McMaster Univ, Dept Math & Stat, Hamilton, ON, Canada

关键词: Determinant;    Permanent;    Zonal and invariant polynomials;    Statistical shape theory;    Elliptical distributions;   

DOI  :  10.1016/j.jmva.2012.07.008

来源: Elsevier

【 摘 要 】

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 matrix-variate 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. (c) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free