Title:Rank, symmetric rank and their decompositions of tensors over arbitrary fields
Speaker:Xiaoyu Song（Harbin Institute of Technology）
Time:Tuesday, November 15, 2022, 9:00-10:00
Location: B201-1, Mingde Building
Abstract：Comon’s Conjecture asserts that for a symmetric tensor, the rank is equal to the symmetric rank. However, the symmetric rank does not always exist. We give a necessary and sufficient condition for symmetric tensors to have symmetric rank, and give some sufficient conditions for this conjecture to be true. Moreover, we propose an algebraic method to compute the symmetric rank and symmetric rank decomposition for symmetric tensors over the binary field. Finally, we completely characterize the maximum rank of m×n×2 tensors over an arbitrary field.
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