If A and B are n-by-n, positive semidefinite Herimitian matrices, then
lambda (min)(AB) less than or equal to lambda (min)(A[alpha ]B[alpha]),
for any phi not equal alpha subset of or equal to {1, 2, ..., n}. A certain
converse is given, as well as analogs for the product of several M-matrice
s and totally nonnegative matrices. However, analogs for lambda (max) (othe
r than the case of totally nonnegative matrices) and for singular values of
general matrices, etc., fail.