Matrix extensions of Liouville-Dirichlet-type integrals |
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Authors: | Ingram Olkin |
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Institution: | Department of Statistics Stanford University Stanford, California 94305 USA |
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Abstract: | The Dirichlet integral provides a formula for the volume over the k-dimensional simplex ω={x1,…,xk: xi?0, i=1,…,k, s?∑k1xi?T}. This integral was extended by Liouville. The present paper provides a matrix analog where now the region becomes , where now each Vi is a p×p symmetric matrix and A?B means that A?B is positive semidefinite. |
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Keywords: | |
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