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Article http://dx.doi.org/10.26855/jamc.2025.12.007

Copositivity of a Class of 4th Order Cyclic Symmetric Tensors

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Min Li

School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China.

*Corresponding author:Min Li

Published: December 31,2025

Abstract

In the context of the big data era, tensor structures capable of carrying high-order and high-dimensional information have increasingly become a research hotspot, and research on tensor theory and its applications across various fields has consequently flourished. Copositivity, as a key property in tensor theory, demonstrates wide application value in multiple important fields such as physics, optimization theory, and machine learning. Cyclic symmetric tensors are a class of tensors with high symmetry, and the study of their copositivity combines both theoretical distinctiveness and practical value. This paper systematically investigates the copositivity of a class of highly symmetric fourth-order three-dimensional cyclic symmetric tensors. Through in-depth analysis of this class of tensors under specific parameter structures, we establish a set of concise inequality relationships between their copositivity and their tensor components, thereby providing a systematic and practical analytical criterion for determining the copositivity of such tensors. This work not only expands the theoretical framework for tensor copositivity verification but also generalizes relevant results from existing research on tensor positive definiteness. Finally, based on the established tensor theoretical results, this paper further derives several (strict) inequalities concerning ternary quartic homogeneous polynomials.

Keywords

Cyclic symmetry; copositive tensors; homogeneous polynomials; ternary quartic forms

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How to cite this paper

Copositivity of a Class of 4th Order Cyclic Symmetric Tensors

How to cite this paper: Min Li. (2025) Copositivity of a Class of 4th Order Cyclic Symmetric Tensors. Journal of Applied Mathematics and Computation, 9(4), 272-277.

DOI: http://dx.doi.org/10.26855/jamc.2025.12.007