{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T19:44:29Z","timestamp":1770752669777,"version":"3.50.0"},"reference-count":37,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T00:00:00Z","timestamp":1755561600000},"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":["12261043"],"award-info":[{"award-number":["12261043"]}],"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 present a Mirsky-type unitarily invariant norm inequality for dual quaternion matrices, which can be regarded as a singular value perturbation theorem for dual quaternion matrices. By using this unitarily invariant norm inequality, we obtain some other unitarily invariant norm inequalities for dual quaternion matrices, including the low-rank approximation problem, eigenvalue perturbation theorem and polar decomposition. Some inequalities for the difference between singular values and eigenvalues of two dual quaternion matrices under the Frobenius norm are extended.<\/jats:p>","DOI":"10.3390\/sym17081355","type":"journal-article","created":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T10:59:01Z","timestamp":1755601141000},"page":"1355","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Mirsky-Type Unitarily Invariant Norm Inequality for Dual Quaternion Matrices and Its Applications"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4150-6334","authenticated-orcid":false,"given":"Jin","family":"Zhong","sequence":"first","affiliation":[{"name":"Faculty of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ping","family":"Zhong","sequence":"additional","affiliation":[{"name":"Faculty of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,19]]},"reference":[{"key":"ref_1","first-page":"381","article-title":"Preliminary sketch of biquaternions","volume":"4","author":"Clifford","year":"1873","journal-title":"Proc. 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