{"id":"https://openalex.org/W2017587562","doi":"https://doi.org/10.1137/s0895479801383877","title":"Means and Averaging in the Group of Rotations","display_name":"Means and Averaging in the Group of Rotations","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2017587562","doi":"https://doi.org/10.1137/s0895479801383877","mag":"2017587562"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479801383877","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479801383877","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049541486","display_name":"Maher Moakher","orcid":"https://orcid.org/0000-0002-9432-0456"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Maher Moakher","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5049541486"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":11.5525,"has_fulltext":false,"cited_by_count":427,"citation_normalized_percentile":{"value":0.99260628,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"24","issue":"1","first_page":"1","last_page":"16"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9825999736785889,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9825999736785889,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9825000166893005,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9814000129699707,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8971302509307861},{"id":"https://openalex.org/keywords/rotation-group-so","display_name":"Rotation group SO","score":0.7305829524993896},{"id":"https://openalex.org/keywords/geometric-mean","display_name":"Geometric mean","score":0.7011849880218506},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.5953323841094971},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5367969274520874},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5101156830787659},{"id":"https://openalex.org/keywords/weighted-geometric-mean","display_name":"Weighted geometric mean","score":0.4976232349872589},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.4943878650665283},{"id":"https://openalex.org/keywords/rotation-matrix","display_name":"Rotation matrix","score":0.4647563695907593},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4343251585960388},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4238434135913849},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35684841871261597},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3259897828102112},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.27166515588760376}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8971302509307861},{"id":"https://openalex.org/C207570611","wikidata":"https://www.wikidata.org/wiki/Q1256500","display_name":"Rotation group SO","level":2,"score":0.7305829524993896},{"id":"https://openalex.org/C40222840","wikidata":"https://www.wikidata.org/wiki/Q185049","display_name":"Geometric mean","level":2,"score":0.7011849880218506},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.5953323841094971},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5367969274520874},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5101156830787659},{"id":"https://openalex.org/C117656884","wikidata":"https://www.wikidata.org/wiki/Q2625569","display_name":"Weighted geometric mean","level":3,"score":0.4976232349872589},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.4943878650665283},{"id":"https://openalex.org/C83633838","wikidata":"https://www.wikidata.org/wiki/Q1256564","display_name":"Rotation matrix","level":2,"score":0.4647563695907593},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4343251585960388},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4238434135913849},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35684841871261597},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3259897828102112},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.27166515588760376},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0895479801383877","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479801383877","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.16.5040","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.16.5040","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://lcvmsun9.epfl.ch/~moakher/simaxpaper.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W158589012","https://openalex.org/W1502435410","https://openalex.org/W1564897360","https://openalex.org/W1566463023","https://openalex.org/W1982559344","https://openalex.org/W1990708122","https://openalex.org/W2005186233","https://openalex.org/W2015952588","https://openalex.org/W2045512849","https://openalex.org/W2061356302","https://openalex.org/W2062459611","https://openalex.org/W2064404969","https://openalex.org/W2097607403","https://openalex.org/W2109409043","https://openalex.org/W2165053603","https://openalex.org/W2496326252","https://openalex.org/W2797466362","https://openalex.org/W2798909945","https://openalex.org/W2904862921","https://openalex.org/W2905505698","https://openalex.org/W3013267890","https://openalex.org/W3217246742","https://openalex.org/W4206628346","https://openalex.org/W4231784839","https://openalex.org/W4232449688","https://openalex.org/W4236700867","https://openalex.org/W4246883249","https://openalex.org/W4251969069","https://openalex.org/W4300222729"],"related_works":["https://openalex.org/W2128177177","https://openalex.org/W2002768246","https://openalex.org/W2288790715","https://openalex.org/W2369650867","https://openalex.org/W2096851309","https://openalex.org/W4254478543","https://openalex.org/W2027369157","https://openalex.org/W2149623705","https://openalex.org/W3151496173","https://openalex.org/W2017587562"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"give":[4,107],"precise":[5],"definitions":[6],"of":[7,12,54,73,75,95,102,113,116],"different,":[8],"properly":[9],"invariant":[10],"notions":[11,115],"mean":[13,18,38,53,60,85,94,101],"or":[14],"average":[15],"rotation.":[16],"Each":[17],"is":[19,41,69],"associated":[20,62],"with":[21,63,91,110],"a":[22,37],"metric":[23,27,66],"in":[24],"SO(3).":[25],"The":[26,59],"induced":[28],"from":[29],"the":[30,44,50,55,64,70,76,83,92,99],"Frobenius":[31],"inner":[32],"product":[33],"gives":[34],"rise":[35],"to":[36,49],"rotation":[39,57,61,78,86],"that":[40,82],"given":[42,56,77],"by":[43],"closest":[45],"special":[46],"orthogonal":[47],"matrix":[48],"usual":[51],"arithmetic":[52],"matrices.":[58,79],"intrinsic":[65],"on":[67],"SO(3)":[68],"Riemannian":[71,84],"center":[72],"mass":[74],"We":[80,106],"show":[81],"shares":[87],"many":[88],"common":[89],"features":[90],"geometric":[93,100],"positive":[96,103],"numbers":[97],"and":[98],"Hermitian":[104],"operators.":[105],"some":[108],"examples":[109],"closed-form":[111],"solutions":[112],"both":[114],"mean.":[117]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":19},{"year":2022,"cited_by_count":18},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":22},{"year":2019,"cited_by_count":20},{"year":2018,"cited_by_count":19},{"year":2017,"cited_by_count":27},{"year":2016,"cited_by_count":19},{"year":2015,"cited_by_count":24},{"year":2014,"cited_by_count":32},{"year":2013,"cited_by_count":30},{"year":2012,"cited_by_count":27}],"updated_date":"2026-06-17T08:01:34.144755","created_date":"2025-10-10T00:00:00"}
