TY - JOUR T1 - Perturbation of the Weighted T-Core-EP Inverse of Tensors Based on the T-Product AU - Liu , Yuhang AU - Ma , Haifeng JO - Communications in Mathematical Research VL - 4 SP - 496 EP - 536 PY - 2021 DA - 2021/08 SN - 37 DO - http://doi.org/10.4208/cmr.2021-0052 UR - https://global-sci.org/intro/article_detail/cmr/19441.html KW - T-product, tensor, perturbation analysis, weighted T-core-EP inverse. AB -

In this paper, we extend the notion of the T-Schur decomposition to the weighted T-core-EP decomposition. Next, the weighted T-core-EP inverse of rectangular tensors is defined by a system, and its existence and uniqueness are obtained. Furthermore, the perturbation of the weighted T-core-EP inverse is studied under several conditions, and the relevant examples are provided to verify the perturbation bounds of the weighted T-core-EP inverse of tensors.