학술논문
Singular random matrix decompositions: Jacobians
Document Type
Article
Source
Subject
*RANDOM matrices
*DETERMINANTS (Mathematics)
*JACOBIAN matrices
*ALGEBRA
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Language
ISSN
0047-259X
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. [Copyright &y& Elsevier]