THE DISTRIBUTIONS OF QUADRATIC FORMS OF RANDOM IDEMPOTENT MATRICES WITH THEIR APPLICATIONS

There have been a few papers on the distribution of quadratic forms of elliptically contoured variables 2, 6, 9. Their results are of particular importance in the theory of the general linear model and distribution, and idempotent metrices play a significant role in the distribution properties of quadratic forms. But in the results of these papers mentioned above the matrices of the quadratic forms have constant elements. The purpose of this paper is to extend some of these results to the case where the elements of the matrices are random variables. Some interesting results are obtained. A few applications of our results are also considered.