SOME FURTHER MATRIX EXTENSIONS OF THE CAUCHY-SCHWARZ AND KANTOROVICH INEQUALITIES, WITH SOME STATISTICAL APPLICATIONS

The well-known Cauchy-Schwarz and Kantorovich inequalities may be expr essed in terms of vectors and a positive definite matrix. We consider what happens to these inequalities when the vectors are replaced by ma trices, the positive definite matrix is allowed to be positive semidef inite singular, and the usual inequalities are replaced by Lowner part ial orderings. Some examples in the context of linear statistical mode ls are presented.