{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T23:47:14Z","timestamp":1781999234992,"version":"3.54.5"},"reference-count":31,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T00:00:00Z","timestamp":1709251200000},"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>Dual quaternions have wide applications in automatic differentiation, computer graphics, mechanics, and others. Due to its application in control theory, matrix equation AXB=C has been extensively studied. However, there is currently limited information on matrix equation AXB=C regarding the dual quaternion algebra. In this paper, we provide the necessary and sufficient conditions for the solvability of dual quaternion matrix equation AXB=C, and present the expression for the general solution when it is solvable. As an application, we derive the \u03d5-Hermitian solutions for dual quaternion matrix equation AXA\u03d5=C, where the \u03d5-Hermitian extends the concepts of Hermiticity and \u03b7-Hermiticity. Lastly, we present a numerical example to verify the main research results of this paper.<\/jats:p>","DOI":"10.3390\/sym16030287","type":"journal-article","created":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T06:07:53Z","timestamp":1709273273000},"page":"287","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["Dual Quaternion Matrix Equation AXB = C with Applications"],"prefix":"10.3390","volume":"16","author":[{"given":"Yan","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Mathematics, Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lv-Ming","family":"Xie","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1825","DOI":"10.1016\/j.sigpro.2009.11.031","article-title":"Local quaternion Fourier transform and color image texture analysis","volume":"90","author":"Assefa","year":"2010","journal-title":"Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1712","DOI":"10.1016\/j.sigpro.2012.12.019","article-title":"A class of quaternion valued affine projection algorithms","volume":"93","author":"Cyrus","year":"2013","journal-title":"Signal Process."},{"key":"ref_3","first-page":"1177","article-title":"Singular value decomposition of matrices of quaternions: A new tool for vector-sensor signal processing","volume":"84","author":"Bihan","year":"2004","journal-title":"IEEE Trans. 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