{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T16:03:50Z","timestamp":1769961830853,"version":"3.49.0"},"reference-count":74,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["OAC-1835443"],"award-info":[{"award-number":["OAC-1835443"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["SII-2029670"],"award-info":[{"award-number":["SII-2029670"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["PHY-2021825"],"award-info":[{"award-number":["PHY-2021825"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2023,6,30]]},"DOI":"10.1137\/21m1416035","type":"journal-article","created":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T18:43:49Z","timestamp":1682534629000},"page":"415-480","source":"Crossref","is-referenced-by-count":6,"title":["Fifty Three Matrix Factorizations: A Systematic Approach"],"prefix":"10.1137","volume":"44","author":[{"given":"Alan","family":"Edelman","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science and AI Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139 USA."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6201-0517","authenticated-orcid":true,"given":"Sungwoo","family":"Jeong","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139 USA."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"351","published-online":{"date-parts":[[2023,4,25]]},"reference":[{"key":"ref1","series-title":"Grad. Texts in Math. 60","volume-title":"Mathematical Methods of Classical Mechanics","author":"Arnold V. I.","year":"2013"},{"key":"ref2","volume-title":"Algebra","author":"Artin M.","year":"2011"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/0029-5582(65)90550-X"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0063334"},{"key":"ref5","first-page":"85","volume":"11","author":"Benner P.","year":"2000","journal-title":"Electron. Trans. Numer. Anal."},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(97)10049-0"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(94)90490-1"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1063\/1.4935852"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1016\/0029-5582(62)90377-2"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2017.09.026"},{"key":"ref11","first-page":"396","volume":"4","author":"Bullock S.","year":"2004","journal-title":"Quantum Inf. Comput."},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1137\/0613028"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(88)90386-X"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.24033\/bsmf.1105"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.24033\/asens.781"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.24033\/bsmf.1113"},{"key":"ref17","first-page":"1","volume":"8","author":"Cartan \u00c9.","year":"1929","journal-title":"J. Math. Pures Appl."},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1969-12330-X"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1137\/0707001"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2022.10.007"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1063\/5.0087010"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2004.12.012"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(78)90058-7"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.2307\/1971201"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2018.02.017"},{"key":"ref27","volume-title":"Lie Groups, Lie Algebras, and Some of Their Applications","author":"Gilmore R.","year":"2012"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.56021\/9781421407944"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1007\/BF02141739"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.2307\/2372674"},{"key":"ref31","volume-title":"Differential Geometry and Symmetric Spaces","author":"Helgason S.","year":"1962"},{"key":"ref32","volume-title":"Differential Geometry, Lie Groups, and Symmetric Spaces","author":"Helgason S.","year":"1978"},{"key":"ref33","volume-title":"Groups and Geometric Analysis: Radon Transforms, Invariant Differential Operators and Spherical Functions","author":"Helgason S.","year":"1984"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144502414930"},{"key":"ref36","volume-title":"The generalized Cartan decomposition for a compact Lie group","author":"Hoogenboom B.","year":"1983"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511840371"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1080\/03081087.2011.618838"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/28.3-4.321"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1134\/S0965542512010034"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.3103\/S0278641918010041"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.24033\/bsmf.90"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1016\/S0301-0104(01)00318-4"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2453-0"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.2969\/jmsj\/05930669"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1007\/s00031-007-0057-4"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.13001\/1081-3810.1148"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.13001\/1081-3810.1101"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1137\/040619363"},{"key":"ref53","volume-title":"A Survey of Matrix Theory and Matrix Inequalities","volume":"14","author":"Marcus M.","year":"1992"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1995.1218"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1997.7123"},{"key":"ref56","first-page":"41","volume":"12","author":"Matsuki T.","year":"2002","journal-title":"J. Lie Theory"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1137\/0609019"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1137\/0718026"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(81)90086-0"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(94)90446-4"},{"key":"ref63","volume-title":"Topics in Quaternion Linear Algebra","author":"Rodman L.","year":"2014"},{"key":"ref64","series-title":"Oxf. Grad. Texts Math. 5","volume-title":"Lie Groups: An Introduction Through Linear Groups","author":"Rossmann W.","year":"2006"},{"key":"ref65","first-page":"201","volume":"17","author":"Sasaki A.","year":"2010","journal-title":"J. Math. Sci. Univ. Tokyo"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1063\/1.532913"},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.1137\/1019104"},{"key":"ref68","doi-asserted-by":"publisher","DOI":"10.1007\/BF01396447"},{"key":"ref69","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0062104"},{"key":"ref70","doi-asserted-by":"publisher","DOI":"10.1137\/050635328"},{"key":"ref71","doi-asserted-by":"publisher","DOI":"10.24033\/bsmf.1598"},{"key":"ref72","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-3820-1"},{"key":"ref73","first-page":"20140585","volume":"471","author":"Townsend A.","year":"2015","journal-title":"Proc. A"},{"key":"ref75","doi-asserted-by":"publisher","DOI":"10.1007\/BF01389653"},{"key":"ref76","volume-title":"Representation of Lie Groups and Special Functions: Volume 3: Classical and Quantum Groups and Special Functions","author":"Vilenkin N. J.","year":"2013"},{"key":"ref77","volume-title":"The Classical Groups: Their Invariants and Representations","author":"Weyl H.","year":"1946"},{"key":"ref78","doi-asserted-by":"publisher","DOI":"10.1016\/B978-1-4832-3188-4.50010-7"},{"key":"ref79","doi-asserted-by":"publisher","DOI":"10.2307\/2371062"},{"key":"ref80","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1964-0170982-7"},{"key":"ref81","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(03)00370-7"},{"key":"ref82","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479802410529"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","deposited":{"date-parts":[[2023,6,30]],"date-time":"2023-06-30T15:04:39Z","timestamp":1688137479000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/21M1416035"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,25]]},"references-count":74,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,6,30]]}},"alternative-id":["10.1137\/21M1416035"],"URL":"https:\/\/doi.org\/10.1137\/21m1416035","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,25]]}}}