Zonal polynomials and hypergeometric functions of quaternion matrix argument

Fei Li; Yifeng Xue

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arXiv · 0901.3379

Zonal polynomials and hypergeometric functions of quaternion matrix argument

Fei Li·Yifeng Xue

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Abstract

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 $W\sim\mathbb{Q}W(n,Σ)$, respectively.

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Fei Li, Yifeng Xue. 2009-01-21. Zonal polynomials and hypergeometric functions of quaternion matrix argument. https://arxiv.org/abs/0901.3379

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