Eigenvalue distributions for some correlated complex sample covariance matrices

Abstract

The distributions of the smallest and largest eigenvalues for the matrix product Z†Z, where Z is an n × m complex Gaussian matrix with correlations both along rows and down columns, are expressed as m × m determinants. In the case of correlation along rows, these expressions are computationally more efficient for the purpose of tabulation than those involving sums over partitions and Schur polynomials reported recently for the same distributions. © 2007 IOP Publishing Ltd.