Latest News

About CAMQ

Information for Authors

Editorial Board

Browse CAMQ Online

Subscription and Pricing

CAMQ Contacts

CAMQ Home

 

Volume 12,     Number 2,     Summer 2004

 

JACOBIANS AND HYPERGEOMETRIC
FUNCTIONS IN COMPLEX MULTIVARIATE
ANALYSIS
T. RATNARAJAH, R. VAILLANCOURT AND M. ALVO

Abstract. In this paper, the Jacobians for complex matrix transformations are derived by means of the exterior product. The transformations are Cholesky factorization, eigen-decomposition and orthonormal-triangular factorization, which frequently occur in complex multivariate analysis. As an example, using these Jacobians we derive the volume of Stiefel manifold and the complex noncentral Wishart density. Moreover, the complex multivariate densities are often represented by complex hypergeometric functions of matrix arguments, which can be expressed in terms of complex zonal polynomials. We give a method to compute these complex hypergeometric functions. Finally, applications of these complex random matrix theories to information theory and numerical analysis are mentioned.

 

Download PDF Files
 
(Subscribers Only)

© 2005, Canadian Applied Mathematics Quarterly (CAMQ)