Characterizations and Perturbations of the Core-EP Inverse of Tensors Based on the T-Product

Abstract

In this paper, we investigate the theory of the core-EP inverse of third-order tensors via the T-product (called T-core-EP inverse). A new decomposition called T-core-EP decomposition of tensors is given by the T-Schur decomposition. A canonical form and some characterizations of the T-core-EP inverse are presented. Finally, we establish the perturbation bounds for the T-core-EP inverse.

Keywords:

• Core-EP inverse
• perturbation
• T-Schur-decomposition
• tensor

AMS SUBJECT CLASSIFICATIONS (2020):

• 15A69
• 15A09

Acknowledgements

We would like to thank Professor M. Zuhair Nashed and three referees for their detailed comments.

Additional information

Funding

This author was supported by the National Natural Science Foundation of China under grant 11971136.