  In a recent paper we have presented a method to evaluate certain Hankel
determinants as almost products; i.e. as a sum of a small number of products.
The technique to find the explicit form of the almost product relies on
differential-convolution equations and trace calculations. In the trace
calculations a number of intermediate nonlinear terms involving determinants
occur, but only to cancel out in the end. In this paper, we introduce a class
of multilinear operators \gamma acting on tuples of matrices as an alternative
to the trace method. These operators do not produce extraneous nonlinear terms,
and can be combined easily with differentiation. The paper is self contained.
An example of an almost product evaluation using \gamma-operators is worked out
in detail and tables of the \gamma-operator values on various forms of matrices
are provided. We also present an explicit evaluation of a new class of Hankel
determinants and conjectures.
