  We resolve a conjecture of Cooper-Fenner-Purewal that a certain sequence of
combinatorial matrices which can be used to bound small product-Ramsey numbers
is positive semidefinite. Because the connection to Ramsey Theory involves
solving quadratic integer programs associated to these matrices, this implies
that there are relatively efficient algorithms for bounding said numbers. The
proof is direct, and yields important structural information: we enumerate the
eigenvalues and eigenspaces explicitly by employing hypergeometric identities.
