The eigenvalues and eigenvectors of nonsingular tensors, similar tensors and tensor products

Abstract

In this paper, we extend some well-known results on the relationships of the eigenvalues and eigenvectors from matrices to the tensors case, including nonsingular tensors and their left (right) inverses, similar tensors, tensor products and , where B is a matrix.

Keywords:

• Tensor
• similar tensors
• Left (right) inverse
• eigenvalue
• eigenvector

AMS Subject Classifications:

• 15A18
• 15A69

Acknowledgements

The author would like to thank the Editor and the referees for their very detailed comments and valuable suggestions which greatly improved the presentation of this paper, and thank Prof. Wen Li for helpful discussions when the author was visiting School of Mathematical Sciences, South China Normal University.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11661036], [grant number 11461026]; the Doctoral Scientific Research Foundation of Chongqing Normal University [grant number 17XLB004].