This monograph is a collective effort by Hamedani and Ghosh which
focuses on a topic which has appeared in many forms: journal articles,
short reviews, books; i.e., characteri- zations of bivariate,
multivariate and matrix variate normal distributions. The first author
is thankful to the second author for his continuous encouragement of
invaluable suggestions in preparing this short monograph. This monograph
attempts to collect all the characteriza- tions results related to a
Gaussian distribution in bivariate and in higher domains that exist in
the literature consequently claims its uniqueness. It also tries to
paint some sketches of the proofs to some of the characterization
results that are not available in the literature as of yet to the best
of the knowledge of the authors. However, the authors do believe that
contributors to this subject matter might have these ideas in their mind
but did not feel nec- essary to pen it down. While this monograph
heavily draws on articles by the second author, Hamedani and his
co-authors in a series of papers, we sincerely hope that the readers and
practitioners in need of an appropriate Gaussian distribution will find
it very useful.