3 problems

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Conjecture on definiteness of separable symmetric tensors
Definiteness conjecture. Then $\mathcal{A}$ is neither a positive semidefinite tensor nor a negative semidefinite tensor.
Conjectureopenpositive-semidefinite-tensors symmetric-tensors tensor-decompositionsarXiv posted 2 days ago
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CPS rank decomposition conjecture for real nonsymmetric fourth-order tensors
Let $\mathcal{A}\in\mathbb{R}_{cps}^{n^4}\backslash\mathbb{R}_s^{n^4}$ be a real fourth-order conjugate partial-symmetric tensor that is not symmetric. A CPS rank decomposition is…
Conjectureopencomplex-tensors positive-semidefinite-tensors tensor-decompositionsarXiv posted 2 days ago
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Conjecture that every M-PSD tensor can be modified into an S-PSD tensor
M-PSD to S-PSD conjecture. Every M-PSD tensor can be modified into an S-PSD tensor while preserving the summations of the corresponding entries.
Conjecturerefutedpositive-semidefinite-tensors strong-ellipticity tensor-analysisarXiv posted 2 days ago

Conjecture on definiteness of separable symmetric tensors