  Calling the quantity; 2delta(A)delta(B)/|<[A, B]>|, with non-zero
denominator, the uncertainty product ratio or UPR for the pair of observables,
(A, B), it is shown that any non-zero correlation coefficient between two
observables raises, above unity, the lower bound of the UPR for each member of
an infinite collection of pairs of incompatible observables. Conversely, any
UPR is subject to lower bounds above unity determined by each of an infinite
collection of correlation coefficients. This result generalizes the well known
Schroedinger strengthening of the Robertson uncertainty relations (with the
former expressed in terms of the correlation coefficient rather than the
anticommutator) where the UPR and the correlation coefficient both involve the
same pair of observables. Two, independent, derivations of the result are
presented to clarify its origins and some examples of its use are examined.
