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We study the scattering matrices employed in time-reversal (TR) imaging algorithms in an attempt to provide additional classification information for scatterers with different shapes and characteristics. Specifically, we apply the eigenspace analysis to the so-called TR operator (TRO) and singular value analysis to the recently introduced space-frequency scattering matrices obtained for metallic and non-metallic objects with different cross-sections, aspect ratios and orientations. It is reported that for scatterers with cross sections less than half wavelength and unity aspect ratios, singular value distributions do not provide enough shape distinguishing information. On the other hand, when the cross-sections are larger and while operating at the higher portion of the frequency spectrum, singular value distributions deviate from each other providing shape distinguishing characteristics.