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...

Assuming that Y has a singular matrix variate elliptically contoured distribution with respect to the Hausdorff measure, the distributions of several matrices associated to QR, modified QR, SV and Polar decompositions of matrix Y are determined, for central and non-central, non-singular and...