Remarks on the positivity of α-determinants

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Abstract

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.

Original languageEnglish
Pages (from-to)169-189
Number of pages21
JournalKyushu Journal of Mathematics
Volume61
Issue number1
DOIs
Publication statusPublished - Jun 7 2007

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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