Positive definiteness of a class of cyclic symmetric tensors

Yisheng Song

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arXiv · 2409.01747

Positive definiteness of a class of cyclic symmetric tensors

Yisheng Song

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Abstract

For a 4th order 3-dimensional cyclic symmetric tensor, a sufficient and necessary condition is bulit for its positive semi-definiteness. A sufficient and necessary condition of positive definiteness is showed for a 4th order $n$-dimensional symmetric tensor. With the help of such a condition, the positive definiteness of a class of 4th order 3-dimensional cyclic symmetric tensors is given. Moreover, the positive definiteness of a class of non-cyclic symmetric tensors is showed also. By applying these conclusions, several (strict) inequalities are erected for ternary quartic homogeneous polynomials.

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Yisheng Song. 2024-09-03. Positive definiteness of a class of cyclic symmetric tensors. https://arxiv.org/abs/2409.01747

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