  Let F be an N x N complex matrix whose jth column is the vector f_j in C^N.
Let |f_j|^2 denote the sum of the absolute squares of the entries of f_j.
Hadamard's inequality for determinants states that |\det(F)| <=
\prod_{j=1}^N|f_j|. Here we prove a sharp upper bound on the permanent of F,
which is |perm(F)| <= N!N^{-N/2} \prod_{j=1}^N|f_j|, and we determine all of
the cases of equality.
