Chapter 5: Matrix-Variate Gamma and Beta Distributions

Abstract

The notations introduced in the preceding chapters will still be followed in this one. Lower-case letters such as x, y will be utilized to represent real scalar variables, whether mathematical or random. Capital letters such as X, Y will be used to denote vector/matrix random or mathematical variables. A tilde placed on top of a letter will indicate that the variables are in the complex domain. However, the tilde will be omitted in the case of constant matrices such as A, B. The determinant of a square matrix A will be denoted as |A| or det(A) and, in the complex domain, the absolute value or modulus of the determinant of B will be denoted as |det(B)|. Square matrices appearing in this chapter will be assumed to be of dimension p × p unless otherwise specified.