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arXiv · 2308.10957

Characteristic polynomials and eigenvalues of tensors

Francesco Galuppi·Fulvio Gesmundo·Ettore Teixeira Turatti·Lorenzo Venturello
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Abstract

We lay the geometric foundations for the study of the characteristic polynomial of tensors. For symmetric tensors of order $d \geq 3$ and dimension $2$ and symmetric tensors of order $3$ and dimension $3$, we prove that only finitely many tensors share any given characteristic polynomial, unlike the case of symmetric matrices and the case of non-symmetric tensors. We propose precise conjectures for the dimension of the variety of tensors sharing the same characteristic polynomial, in the symmetric and in the non-symmetric setting.

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Francesco Galuppi, Fulvio Gesmundo, Ettore Teixeira Turatti, Lorenzo Venturello. 2023-08-21. Characteristic polynomials and eigenvalues of tensors. https://arxiv.org/abs/2308.10957

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