Singular random matrix decompositions: Jacobians

descriptionPublicationkeyboard_double_arrow_right Article , Research , Preprint 01 Apr 2005 English Publisher:Elsevier BVJournal:Journal of Multivariate Analysis, volume 93, pages 296-312 (issn: 0047-259X,

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Authors: González Farías, Graciela; Díaz García, José A.;

doi: 10.1016/j.jmva.2004.03.002

handle: 10016/184

Singular random matrix decompositions: Jacobians

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Abstract

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

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Keywords

L′DM and polar decompositions, Statistics and Probability, symmetric nonnegative definite square root decomposition, Random matrices (algebraic aspects), Estadística, Direct numerical methods for linear systems and matrix inversion, random matrices, Factorization of matrices, Hausdorff measure, L′DL, Cholesky decompositions, Numerical Analysis, Spectral, singular distribution, Singular distribution, QR factorization, L′U, QR, Symmetric nonnegative definite square root, spectral decomposition, \(L'U\) factorization, Statistics, Probability and Uncertainty, SVD, polar singular value decomposition

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