Exact Joint Distributions of Few Roots of a Class of Random Matrices.

In this paper, the authors derived the exact expression for the joint marginal density of any few consecutive ordered roots of a class of random matrices. In addition, the authors obtained an expression for the probability integral associated with the joint distribution of any two ordered roots. The class of random matrices considered includes Wishart matrix, multivariate analysis of variance matrix and canonical correlation matrix. The authors also obtained an expression for the joint density of any two unordered roots of the above class of random matrices. Some of these results are useful in reduction of dimensionality in pattern recognition problems, and the statisitical analysis of energy levels of certain complicated systems in physics. Author