TY - JOUR
T1 - Determinants, permanents and some applications to statistical shape theory
AU - Caro-Lopera, Francisco J.
AU - González-Farías, Graciela
AU - Balakrishnan, N.
PY - 2013/1/1
Y1 - 2013/1/1
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.
U2 - 10.1016/j.jmva.2012.07.008
DO - 10.1016/j.jmva.2012.07.008
M3 - Article
SN - 0047-259X
VL - 114
SP - 29
EP - 39
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
IS - na
ER -