Some classes of nonsingular tensors and application

Abstract

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.

Keywords:

• Tensor
• C-tensor
• $C_{\pi }^R$-tensor
• $B_{\pi }^R$-tensor
• nonsingular tensor

Acknowledgments

The authors are grateful to the referees for their useful and constructive suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by New Academic Talents and Innovative Exploration Fostering Project in China (Qian Ke He Pingtai Rencai[2017]5727-21), Guizhou Province Natural Science Foundation in China (Qian Jiao He KY [2020]094), Science and Technology Foundation of Guizhou Province, China (Qian Ke He Ji Chu ZK[2021]Yi Ban 014), General Project of Philosophy and Social Sciences Planning in Guizhou Province (19GZYB11).