International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 2, Pages 341-346

A characterization of matrix variate normal distribution

Khoan T. Dinh1 and Truc T. Nguyen2

1US Environmental Protection Agency/TS 798, Washington, DC 20460, USA
2Department of Mathematics and Statistics, Bowling Green State University, Bowling Green 43403-0221, OH, USA

Received 31 December 1992; Revised 26 June 1993

Copyright © 1994 Khoan T. Dinh and Truc T. Nguyen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The joint normality of two random vectors is obtained based on normal conditional with linear regression and constant covariance matrix of each vector given the value of the other without assuming the existence of the joint density. This result is applied to a characterization of matrix variate normal distribution.