ABSTRACT
This chapter presents results on expected values of functions of quadratic forms. It derives some distributions of functions of positive definite matrix quadratic forms. These distributions are useful in deriving the distribution of characteristic roots, which are fundamental in the study of multivariate tests. The chapter highlights series representations of the density of the quadratic form, and derives noncentral density function. It gives conditions for Wishartness of quadratic forms of the type XAX'. Conditions for independence of two or more such quadratic forms are also given. The chapter derives similar conditions for the quadratic forms of the type XAX'+12(LX'+XL')+C. It proves some theorems about the stochastic independence of quadratic forms of the type XAX'. The chapter discusses conditions for Wishartness and independence of quadratic forms which are generalizations of the quadratic forms of the type XAX'.
