The Distribution of the Latent Roots of the Covariance Matrix
Alan T. James · The Annals of Mathematical Statistics · 1960
The distribution of the latent roots of the covariance matrix calculated from a sample from a normal multivariate population, was found by Fisher [3], Hsu [6] and Roy [10] for the special, but important case when the population covariance matrix is a scalar matrix, $\Sigma = \sigma^2I$. By use of the representation theory of the linear group, we are able to obtain the general distribution for arbitrary $\Sigma$.