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<p>For a fourth order three-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 fourth order <i>n</i>-dimensional symmetric tensor. With the help of such a condition, the positive definiteness of a class of fourth order three-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.</p>

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Positive Definiteness of a Class of Cyclic Symmetric Tensors

  • 期刊论文

  • 发表日期：

    2025年1月30日

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  • Yisheng Song

摘要

For a fourth order three-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 fourth order n-dimensional symmetric tensor. With the help of such a condition, the positive definiteness of a class of fourth order three-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.