The analytic criterion of strict copositivity for a 4th-order 3-dimensional tensor

This paper focuses on the strict copositivity analysis of 4th-order 3-dimensional symmetric tensors. A necessary and sufficient condition is provided for the strict copositivity of a fourth-order symmetric tensor. Subsequently, building upon this conclusion, we discuss the strict copositivity of fourth-order three-dimensional symmetric tensors with its entries $\pm 1,0$, and further build their necessary and sufficient conditions. Utilizing these theorems, we can effectively verify the strict copositivity of a general fourth-order three-dimensional symmetric tensors.