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Kyushu Journal of Mathematics
Vol. 61 (2007) No. 1 P 169-189



We give a probabilistic expression of the α-determinant by using the Wishart distribution on the cone of positive definite matrices. As a corollary, we give a partial answer to a positivity problem for the α-determinant which is equivalent to the existence problem of certain multivariate probability distributions. We also give a concrete example to support our conjecture for the positivity.

Copyright © 2007 by Faculty of Mathematics, Kyushu University

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