Matrix derivatives and its applications in statistics

The scalar values of differentials rather than symbolic derivatives are treated here. This approach simplifies the differential calculus in statistics because, often, the linear representations of differentials in statistics (1) are complicated, (2) depend on the bases used, (3) can be obtained by the scalar values on elements of a given basis, and (4) are not necessary for many problems of finding maxima and minima. Among others, a product rule is obtained in a very general and simple form. The results are applied to certain problems in multivariate statistical analysis that are useful to psychology and other behavioral sciences.