Range-space based identification aims at the recovery of a linear system (e.g multi-FIR channel identification for deblurring) by its output span, and constraints on its structure, often given by explicit parameterization. A key question for this inverse problem is under what conditions the recovered system is unique. When the parametrization is polynomial, algebraic geometry is a natural apparatus to analyze this problem. In this paper, we show that the collection of all non-identifiable parameters form an algebraic variety in the parameter space, which under certain conditions is nowhere dense. This allows to develop a simple numerical test to guarantee identifiability of certain parametric families of linear systems.