Moments and Quadratic Forms of Matrix Variate Skew Normal Distribution

In 2007, Dominguez-Molina etal. obtained the moment generating function (mgf) of the matrix variate closed skew normal distribution. In this paper, we use their mgf to obtain the first two moments and some additional properties of quadratic forms for the matrix variate skew normal distributions. The quadratic forms are particularly interesting because they are essentially correlation tests that introduce a new type of orthogonality condition.