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On surface integrals related to distributions of random matrices

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Abstract

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

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Authors and Affiliations

  1. Higher School of Economics, National Research University, Moscow, Russia

    A. S. Shvedov

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  1. A. S. Shvedov
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Correspondence to A. S. Shvedov.

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__________

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 53, No. 1, pp. 222–235, January–February, 2012.

Original Russian Text Copyright © 2012 Shvedov A. S.

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Shvedov, A.S. On surface integrals related to distributions of random matrices. Sib Math J 53, 182–192 (2012). https://doi.org/10.1134/S0037446612010168

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  • DOI: https://doi.org/10.1134/S0037446612010168

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