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 $n\times m$ complex Gaussian matrix with correlations both along rows and down columns, are expressed as $m\times m$ determinants. In the case of correlation along rows, these expressions are computationally more efficient than those involving sums over partitions and Schur polynomials reported recently for the same distributions.

11 pages