The concept of $C_{\pi }^R$-matrix is extended to $C_{\pi }^R$-tensor, which also generalizes the concept of C-tensor. A necessary and sufficient condition for a tensor to be a $C_{\pi }^R$-tensor is provided. We analyse decompositions of $C_{\pi }^R$-tensors and prove that $C_{\pi }^R$-tensors are nonsingular. Positive linear combinations and Hadamard product of two $C_{\pi }^R$-tensors are also discussed. Finally, some properties of $B_{\pi }^R$-tensor are given to localize real eigenvalues of a tensor.

中文翻译：

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几类非奇异张量及其应用

的概念$C_{\pi }^R$-矩阵扩展为$C_{\pi }^R$-tensor，它也概括了C -tensor 的概念。张量成为a的充分必要条件$C_{\pi }^R$-提供张量。我们分析分解$C_{\pi }^R$-张量并证明$C_{\pi }^R$-张量是非奇异的。正线性组合和两个的 Hadamard 乘积$C_{\pi }^R$- 还讨论了张量。最后，一些属性${乙}_{\pi }^R$-张量用于定位张量的实特征值。