  This paper is devoted to a generalization of a Hadamard type inequality for
the permanent of a complex square matrix. Our proof is based on a non-trivial
extension of a technique used in Carlen, Lieb and Loss (Methods and
Applications of Analysis 13 (1) (2006) 1-17). We give an application to
coefficients of products of linear forms and show some auxiliary inequalities,
which might be of independent interest.
