The 70th anniversary of the distribution of random matrices: A survey Original Research Article

Although distribution theory dates back over a century, the distributions derived were essentially univariate. The distribution of the sample covariance matrix was perhaps the beginning of a theory of distributions of random matrices. When the underlying distribution is multivariate normal, the distribution of the sample covariance matrix is the Wishart distribution. We here provide a review of the distribution of a variety of matrices as they arise from matrix factorizations.