{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T19:06:59Z","timestamp":1770750419704,"version":"3.50.0"},"reference-count":26,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,10]],"date-time":"2025-02-10T00:00:00Z","timestamp":1739145600000},"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>In this paper, we explore the least-norm solution to the classical matrix equation AXB=C over the dual quaternion algebra, where A, B, and C are given matrices, while X remains the unknown matrix. We begin by transforming the definition of the Frobenius norm for dual quaternion matrices into an equivalent form. Using this new expression, we investigate the least-norm solution to the equation AXB=C under solvability conditions. Additionally, we examine the minimum real part of the norm solution in cases where a least-norm solution does not exist. Finally, we provide two numerical examples to illustrate the main findings of our study.<\/jats:p>","DOI":"10.3390\/sym17020267","type":"journal-article","created":{"date-parts":[[2025,2,10]],"date-time":"2025-02-10T06:43:07Z","timestamp":1739169787000},"page":"267","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["The Least-Norm Solution to a Matrix Equation over the Dual Quaterion Algebra"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-9032-6689","authenticated-orcid":false,"given":"Ling-Jie","family":"Zhu","sequence":"first","affiliation":[{"name":"Department of Mathematics and Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0189-5355","authenticated-orcid":false,"given":"Qing-Wen","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China"},{"name":"Collaborative Innovation Center for the Marine Artificial Intelligence, Shanghai University, Shanghai 200444, China"}]},{"given":"Zu-Liang","family":"Kou","sequence":"additional","affiliation":[{"name":"Shanghai Newtouch Software Co., Ltd., Shanghai 200127, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,10]]},"reference":[{"key":"ref_1","unstructured":"Grattan-Guinness, I., Cooke, R., Corry, L., Cr\u00e9pel, P., and Guicciardini, N. 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