The Haar measure and the generation of random unitary matrices
Paper in proceedings, 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.