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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.
}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2021-0052}, url = {http://global-sci.org/intro/article_detail/cmr/19441.html} }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.