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Strongly Positive Semi-Definite and Strongly SOS Tensors

Odd-order symmetric tensors whose induced vector map F(x)=Ax^(m-1) is entrywise nonnegative (strongly PSD) or entrywise a sum of squares (strongly SOS), together with the wider classes of generalized and genuinely positive semi-definite tensors and the H-eigenvalue-free 'barren' tensors that separate them.

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Strongly Positive Semi-Definite Tensors and Strongly SOS Tensors Liqun Qi∗ Chunfeng Cui† January 7

Introduces odd-order strongly positive semi-definite (PSD) and strongly sum-of-squares (SOS) tensors. An odd-order symmetric tensor A is strongly PSD if the vector map F(x)=Ax^(m-1) is entrywise nonn…