Matrix Variate Normal Distribution

This chapter discusses matrix variate normal distribution, which is one of the most important matrix variate distributions. The matrix variate normal distribution arises when sampling from multivariate normal population. The chapter describes various properties of matrix variate normal distribution. A way of extending the concept of normal distribution was shown by Goodman and Kotz. They introduced the multivariate θ-generalized normal distribution. Linear transformations of matrices with matrix variate θ-generalized normal distribution have matrix variate θ-generalized normal distribution. The chapter generalizes a result of Basu and Khatri for the matrix variate normal case. It defines the symmetric matrix variate normal distribution. The chapter derives the first four moments of a matrix variate θ-generalized normal distribution. Matrix variate θ-generalized normal distributions have maximal entropy in certain class of distributions.