{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,21]],"date-time":"2025-08-21T17:47:19Z","timestamp":1755798439753,"version":"3.44.0"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"12","license":[{"start":{"date-parts":[[2024,9,12]],"date-time":"2024-09-12T00:00:00Z","timestamp":1726099200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[2024,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Kinematics remains one of the cornerstones of robotics, and over the decade, Robotica has been one of the venues in which groundbreaking work in kinematics has always been welcome. A number of works in the kinematics community have addressed metrics for rigid-body motions in multiple different venues. An essential feature of any distance metric is the triangle inequality. Here, relationships between the triangle inequality for kinematic metrics and so-called trace inequalities are established. In particular, we show that the Golden-Thompson inequality (a particular trace inequality from the field of statistical mechanics) which holds for Hermitian matrices remarkably also holds for restricted classes of real skew-symmetric matrices. We then show that this is related to the triangle inequality for <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0263574724000778_inline1.png\"\/><jats:tex-math>\n$SO(3)$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0263574724000778_inline2.png\"\/><jats:tex-math>\n$SO(4)$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> metrics.<\/jats:p>","DOI":"10.1017\/s0263574724000778","type":"journal-article","created":{"date-parts":[[2025,4,14]],"date-time":"2025-04-14T05:55:56Z","timestamp":1744610156000},"page":"4103-4119","source":"Crossref","is-referenced-by-count":0,"title":["Trace inequalities and kinematic metrics"],"prefix":"10.1017","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-4383-8748","authenticated-orcid":false,"given":"Yuwei","family":"Wu","sequence":"first","affiliation":[{"name":"National University of Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0542-9028","authenticated-orcid":false,"given":"Gregory S.","family":"Chirikjian","sequence":"additional","affiliation":[{"name":"National University of Singapore"},{"name":"University of Delaware"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2024,9,12]]},"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574724000778","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T07:52:08Z","timestamp":1755589928000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574724000778\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,12]]},"references-count":0,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2024,12]]}},"alternative-id":["S0263574724000778"],"URL":"https:\/\/doi.org\/10.1017\/s0263574724000778","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"type":"print","value":"0263-5747"},{"type":"electronic","value":"1469-8668"}],"subject":[],"published":{"date-parts":[[2024,9,12]]}}}