  The Empirical Interpolation Method (EIM) is a greedy procedure that
constructs approximate representations of two-variable functions in separated
form. In its classical presentation, the two variables play a non-symmetric
role. In this work, we give an equivalent definition of the EIM approximation,
in which the two variables play symmetric roles. Then, we give a proof for the
existence of this approximation, and extend it up to the convergence of the
EIM, and for any norm chosen to compute the error in the greedy step. Finally,
we introduce a way to compute a separated representation in the case where the
number of selected values is different for each variable. In the case of a
physical field measured by sensors, this is useful to discard a broken sensor
while keeping the information provided by the associated selected field.
