Date of Award


Publication Type

Doctoral Thesis

Degree Name



Mathematics and Statistics




Tracy, Derrick S.,




Moments of multivariate and matrix-variate distributions are obtained for both complex and real cases by differentiating their characteristic functions (c.f.) using matrix derivatives. The complex differential operators for functions of complex matrices and vectors are developed by extending the scalar complex differential operators. Applying these operators, a recurrence relation for the derivatives of c.f. of the generalized complex matrix-variate normal distribution is obtained. Explicit expressions for the moments of order 2k, k $\ge$ 1, are also obtained. From these expressions, as special cases, the corresponding results for complex matrix-variate normal, complex multivariate normal distributions are obtained. When imaginary parts of complex matrices are replaced by null matrices, we obtain the above results for real cases for generalized matrix-variate normal and multivariate normal distributions. The moments of complex and real matrix quadratic forms up to order three are calculated by using the moments of complex and real matrix-variate normal distributions and employing the properties of Kronecker products and commutation matrices. From these the moments of complex and real central and noncentral Wishart distributions are obtained as special cases. Moments of Hermitian and real quadratic forms are also obtained.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1994 .S84. Source: Dissertation Abstracts International, Volume: 56-11, Section: B, page: 6214. Adviser: Derrick S. Tracy. Thesis (Ph.D.)--University of Windsor (Canada), 1995.