Volume 37, Issue 4
Perturbation of the Weighted T-Core-EP Inverse of Tensors Based on the T-Product

Yuhang Liu & Haifeng Ma

Commun. Math. Res., 37 (2021), pp. 496-536.

Published online: 2021-08

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  • Abstract

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.

  • Keywords

T-product, tensor, perturbation analysis, weighted T-core-EP inverse.

  • AMS Subject Headings

15A69, 65F10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-37-496, author = {Liu , Yuhang and Ma , Haifeng}, title = {Perturbation of the Weighted T-Core-EP Inverse of Tensors Based on the T-Product}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {37}, number = {4}, pages = {496--536}, abstract = {

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} }
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.

Yuhang Liu & HaifengMa. (2021). Perturbation of the Weighted T-Core-EP Inverse of Tensors Based on the T-Product. Communications in Mathematical Research . 37 (4). 496-536. doi:10.4208/cmr.2021-0052
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