The Haar measure and the generation of random unitary matrices

Paper i proceeding, 2004

This paper derives thc Haar measure over the set of unitary matrices. The Haar measure is essential when studying the statistical bchavior of complex sample covariance matrices in terms of their cigenvalucs and eigenvectors. The _. characterization is based on Murnaghans parameterization of unitary matrices which can be seen as a generalization of the representation of orthogonal matrices using Givens rotations. In addition to deriving the Haar measure, an efficient method to obtain samples from it is also presented.