Eigenvalue distributions for some correlated complex sample covariance matrices

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 than those involving sums over partitions and Schur polynomials reported recently for the same distributions.