Blind Identification of Under-Determined Mixtures (UDM) is involved in numerous applications, including Multi-Way factor Analysis (MWA) and Signal Processing. In the latter case, the use of High-Order Statistics (HOS) like Cumulants leads to the decomposition of symmetric tensors. Yet, little has been published about rank-revealing decompositions of symmetric tensors. Definitions of rank are discussed, and useful results on Generic Rank are proved, with the help of tools borrowed from Algebraic Geometry. 1
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