CANONICAL CORRELATIONS ASSOCIATED WITH SYMMETRICAL REFLEXIVE GENERALIZED INVERSES OF THE DISPERSION MATRIX

We consider the relations between two sets of canonical correlations: one based on a (possibly singular) dispersion matrix V, and the other on a symmetric reflexive generalized inverse of V. Special attention is paid to the number of unit canonical correlations in each set. We establish series of results characterizing the situations where all canonical correlations in one or both sets are less than one. It tums out that in all such situations the canonical correlations in the one set are uniformly comparable to those in the other set.