Invariant relationships involving ratios of determinants have been proposed for the classification of an object in SAR imagery. The target detection decision-making process depends on the uncertainty involved in the measurements. At fixed experimental resolution, some determinants are simply better than others because they are much less sensitive to uncertainty. A geometrical interpretation of determinants is applied to assess the minimum relative uncertainty expected for a determinant employed in invariant relationships. Because much larger relative uncertainties can occur in some determinants, a method based on the perturbation of eigenvalues is proposed to identify determinants that are less sensitive to element errors. Symmetric alpha-stable probability distribution functions are employed to characterize error distributions in ratios of determinants.