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Genericity And Rank Deficiency Of High Order Symmetric Tensors

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