Abstract
In this paper, we give the Jacobians of matrix transformations and when the constant matrices A and are singular rectangular matrices, not limited to square matrices, and the random variables in the random matrices X, Y can be linearly dependent, W and are singular random matrices. Furthermore, some important properties about singular multivariate Normal distribution and singular Wishart distribution are proved by using these Jacobians. Finally, the density function of and the distribution of generalized Hotelling’s T 2 statistic are obtained.
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