Polarimetric Analysis Using the Algebraic Real Representation of the Scattering Matrix

Equivalent matrix representations in radar polarimetry have long been studied and used as tools for modeling and understanding the scattering mechanisms. We include here the Kennaugh, Graves, or covariance matrices which are today seen as alternative representations of the same physical quantity, the scattering matrix. In this paper, we briefly explore some of the properties of the algebraic real representation of a complex matrix, a mathematical construction which has been introduced in the literature as an alternative way of performing consimilarity transformations (rather than by the usual Graves power decomposition, with applications limited only to those involving symmetric scattering matrices). Besides the theoretical presentation on the subject, the main goals of the paper are to study some of the advantages and limitations of using the 4 × 4 real matrix form and to compare consimilarity transformation results obtained through the real representation to those given by the power representation.