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The Haar measure and the generation of random unitary matrices

Magnus Lundberg (Institutionen för signaler och system, Signalbehandling) ; Lennart Svensson (Institutionen för signaler och system, Signalbehandling)
2004 Sensor Array and Multichannel Signal Processing Workshop; Barcelona; Spain; 18 July 2004 through 21 July 2004 p. 114-118. (2004)
[Konferensbidrag, refereegranskat]

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.



Denna post skapades 2010-05-12. Senast ändrad 2017-01-27.
CPL Pubid: 121542

 

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Institutioner (Chalmers)

Institutionen för signaler och system, Signalbehandling (1900-2017)

Ämnesområden

Matematisk statistik

Chalmers infrastruktur