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<p>This paper focuses on the strict copositivity of fourth-order three-dimensional symmetric tensors. A necessary and sufficient condition is provided for the strict copositivity of a fourth-order symmetric tensor. Subsequently, we discuss the strict copositivity of fourth-order three-dimensional symmetric tensors with their entries <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\pm 1, 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>±</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> and further build their necessary and sufficient conditions. Utilizing these theorems, we can effectively verify the strict copositivity of general fourth-order three-dimensional symmetric tensors.</p>

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Strict Copositivity for a Class of Fourth-Order Three-Dimensional Tensors

  • 期刊论文

  • 发表日期：

    2026年7月28日

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  • Mingjun Sheng,
  • Yisheng Song

摘要

This paper focuses on the strict copositivity of fourth-order three-dimensional symmetric tensors. A necessary and sufficient condition is provided for the strict copositivity of a fourth-order symmetric tensor. Subsequently, we discuss the strict copositivity of fourth-order three-dimensional symmetric tensors with their entries \(\pm 1, 0\) ± 1 , 0 and further build their necessary and sufficient conditions. Utilizing these theorems, we can effectively verify the strict copositivity of general fourth-order three-dimensional symmetric tensors.