{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:33:04Z","timestamp":1760149984780,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T00:00:00Z","timestamp":1695859200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Research Fund Project of Guangxi University for Nationalities","award":["2019KJQD03","GUIJIAOSHIFAN2019-81HAO","12061015"],"award-info":[{"award-number":["2019KJQD03","GUIJIAOSHIFAN2019-81HAO","12061015"]}]},{"name":"Thousands of Young and Middle-aged Key Teachers Training Programme in Guangxi Colleges and Universities","award":["2019KJQD03","GUIJIAOSHIFAN2019-81HAO","12061015"],"award-info":[{"award-number":["2019KJQD03","GUIJIAOSHIFAN2019-81HAO","12061015"]}]},{"name":"National Natural Science Foundation of China","award":["2019KJQD03","GUIJIAOSHIFAN2019-81HAO","12061015"],"award-info":[{"award-number":["2019KJQD03","GUIJIAOSHIFAN2019-81HAO","12061015"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we extend the BT inverse to the set of third-order tensors, and we call it the T-BT inverse. We give characterizations and properties of the inverse by applying tensor decomposition. Based on the inverse, we introduce a new binary relation: T-BT order. Furthermore, by applying the T-BT order, we introduce a generalized core partial order (called T-GC partial order).<\/jats:p>","DOI":"10.3390\/axioms12100929","type":"journal-article","created":{"date-parts":[[2023,9,29]],"date-time":"2023-09-29T07:42:08Z","timestamp":1695973328000},"page":"929","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["T-BT Inverse and T-GC Partial Order via the T-Product"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2569-0821","authenticated-orcid":false,"given":"Hongxing","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematics and Physics, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi Minzu University, Nanning 530006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Wen","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi Minzu University, Nanning 530006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1080\/03081087.2015.1083933","article-title":"Moore-Penrose inverse of tensors via Einstein product","volume":"64","author":"Sun","year":"2016","journal-title":"Linear Multilinear Algebra"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1662","DOI":"10.1080\/03081087.2016.1253662","article-title":"Further results on generalized inverses of tensors via the Einstein product","volume":"65","author":"Behera","year":"2017","journal-title":"Linear Multilinear Algebra"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1016\/j.laa.2010.09.020","article-title":"Factorization strategies for third-order tensors","volume":"435","author":"Kilmer","year":"2011","journal-title":"Linear Algebra Its Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s42967-019-00055-4","article-title":"T-Jordan canonical form and T-Drazin inverse based on the T-product","volume":"3","author":"Miao","year":"2021","journal-title":"Commun. 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