Determinants, permanents and some applications to statistical shape theory

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

Research output: Contribution to journalArticlepeer-review


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.
Original languageAmerican English
Pages (from-to)29-39
Number of pages11
JournalJournal of Multivariate Analysis
Issue numberna
StatePublished - 1 Jan 2013


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