Singular random matrix decompositions: Jacobians

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 nonnegat...

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Bibliographic Details
Published in:Journal of multivariate analysis 2005-04, Vol.93 (2), p.296-312
Main Authors: Dı́az-Garcı́a, José A., González-Farı́as, Graciela
Format: Article
Language:English
Subjects:
Cholesky decompositions
Hausdorff measure
Hausdorff measure Singular distribution SVD QR L'U L'DM and polar decompositions Spectral L'DL Cholesky decompositions Symmetric nonnegative definite square root
L′ DL
L′ DM and polar decompositions
L′ U
Mathematical models
Matrix
Singular distribution
Spectral
Studies
SVD
Symmetric nonnegative definite square root
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Summary: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.
ISSN:0047-259X
1095-7243
DOI:10.1016/j.jmva.2004.03.002