Zonal polynomials and hypergeometric functions of quaternion matrix argument

Details Zonal polynomials and hypergeometric functions of quaternion matrix argument Zonal polynomials and hypergeometric functions of quaternion matrix argument

2009-01-21

arxiv.org/abs/0901.3379v1

Mathematics

Statistics Theory

22 pages. Communications in Statistics - Theory and Methods (appear)

Scientific paper

We define zonal polynomials of quaternion matrix argument and deduce some
important formulae of zonal polynomials and hypergeometric functions of
quaternion matrix argument. As an application, we give the distributions of the
largest and smallest eigenvalues of a quaternion central Wishart matrix
$W\sim\mathbb{Q}W(n,\Sigma)$, respectively.

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