Singular random matrix decompositions: Jacobians

Authors:
José A. Díaz-García;Graciela González-Farías
Affiliations:
Dept. of Stats. and Comp., Universidad Autónoma Agraria Antonio Narro, 25315 Buenavista, Saltillo, Coahuila, Mexico and Dept. of Prob. and Stats. of the Centro de Investigación en Mathem ...;Department of Probability and Statistics, Centro de Investigación en Matemáticas, Callejón de Jalisco s/n, Mineral de Valenciana, 36240 Guanajuato, Mexico
Venue:
Journal of Multivariate Analysis
Year:
2005

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Abstract

For a singular random matrix X, we find the Jacobians associated to the following decompositions: QR, Polar, Singular Value (SVD), L'U, L'DM and modified QR (QDR). Similarly, for the cross-product matrix S = X'X we find the Jacobians of the Spectral, Cholesky's, L'DL and symmetric nonnegative definite square root decompositions.