On surface integrals related to distributions of random matrices

A. S. Shvedov

National Research University "Higher School of Economics", Moscow

Abstract: We construct the first quadratic form and the volume element of the surface consisting of all positive semidefinite $m\times m$ matrices of rank $r$ with $r$ distinct positive eigenvalues. We give the density function of the singular gamma distribution.

Keywords: first quadratic form, volume element, singular gamma distribution, random matrix.

UDC: 514.7+517.3+519.2

Received: 14.04.2010

 English version: Siberian Mathematical Journal, 2012, 53:1, 182–192

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