Quadratic and Bilinear Forms In Normal Vectors

Abstract

Mathai and Provost (1992) dealt with quadratic forms in random variables, their distributions, moments and various properties including chisquaredness. In this chapter we will concentrate on bilinear forms in random variables and their properties. Generalizations to matrix variables will be dealt with in detail in Chapters 4 and 5 but some aspects of matrix variables will also be considered in this chapter. Even though a bilinear form can be considered to be a particular case of a quadratic form, the general methods of tackling quadratic forms can sometimes become too complicated to handle bilinear forms. In these cases specific techniques are to be developed for dealing with bilinear forms. This will be seen from the discussions later on in this chapter. The material in this as well as in the remaining chapters will complement that in Mathai and Provost (1992).