THE ESSENTIAL THEORY OF THE QUADRATIC FORMS OF THE WISHART MATRIX AND ITS APPLICATION

Suppose that A～W_m（n,Σ）,D is m×m symmetric matrix, B=A'DA is called the quadratic forms of the "Wishart matrix. In this paper, the density function, the expectation, and the other essential properties of B are obtained. The above results can also be extended into spherical and elliptical distributions. At last, the theory of the quatlratic forms of Wishart matrix is applied to the Bayes estimation of the coyariance matrix Σ in normal population.