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Eigenvalue distributions for some correlated complex sample covariance matrices

P. J. Forrester
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Abstract

The distributions of the smallest and largest eigenvalues for the matrix product $Z^\dagger Z$, 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.

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P. J. Forrester. 2006-01-31. Eigenvalue distributions for some correlated complex sample covariance matrices. https://doi.org/10.1088/1751-8113/40/36/009

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