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Determinants, permanents and some applications to statistical shape theory

Author

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

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 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.

Suggested Citation

  • Caro-Lopera, Francisco J. & González-Farías, Graciela & Balakrishnan, N., 2013. "Determinants, permanents and some applications to statistical shape theory," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 29-39.
    • Handle: RePEc:eee:jmvana:v:114:y:2013:i:c:p:29-39
    DOI: 10.1016/j.jmva.2012.07.008
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    References listed on IDEAS

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    1. Caro-Lopera, Francisco J. & Díaz-García, José A. & González-Farías, Graciela, 2010. "Noncentral elliptical configuration density," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 32-43, January.
    2. José Díaz-García & Francisco Caro-Lopera, 2012. "Generalised shape theory via SV decomposition I," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(4), pages 541-565, May.
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