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.
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