{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T17:09:30Z","timestamp":1778605770168,"version":"3.51.4"},"reference-count":28,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,3,17]],"date-time":"2024-03-17T00:00:00Z","timestamp":1710633600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12371023"],"award-info":[{"award-number":["12371023"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper considers the Hermitian solutions of a new system of commutative quaternion matrix equations, where we establish both necessary and sufficient conditions for the existence of solutions. Furthermore, we derive an explicit general expression when it is solvable. In addition, we also provide the least squares Hermitian solution in cases where the system of matrix equations is not consistent. To illustrate our main findings, in this paper we present two numerical algorithms and examples.<\/jats:p>","DOI":"10.3390\/sym16030361","type":"journal-article","created":{"date-parts":[[2024,3,18]],"date-time":"2024-03-18T05:14:07Z","timestamp":1710738847000},"page":"361","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["The Hermitian Solution to a New System of Commutative Quaternion Matrix Equations"],"prefix":"10.3390","volume":"16","author":[{"given":"Yue","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Mathematics, Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0189-5355","authenticated-orcid":false,"given":"Qing-Wen","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China"},{"name":"Collaborative Innovation Center for the Marine Artificial Intelligence, Shanghai 200444, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lv-Ming","family":"Xie","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,17]]},"reference":[{"key":"ref_1","unstructured":"Hamilton, W.R. 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