{"id":"https://openalex.org/W4392386288","doi":"https://doi.org/10.3390/sym16030287","title":"Dual Quaternion Matrix Equation AXB = C with Applications","display_name":"Dual Quaternion Matrix Equation AXB = C with Applications","publication_year":2024,"publication_date":"2024-03-01","ids":{"openalex":"https://openalex.org/W4392386288","doi":"https://doi.org/10.3390/sym16030287"},"language":"en","primary_location":{"id":"doi:10.3390/sym16030287","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16030287","pdf_url":"https://www.mdpi.com/2073-8994/16/3/287/pdf?version=1709289124","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/16/3/287/pdf?version=1709289124","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114549847","display_name":"Yan Chen","orcid":"https://orcid.org/0000-0003-4838-3779"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan Chen","raw_affiliation_strings":["Department of Mathematics, Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100771668","display_name":"Qing\u2010Wen Wang","orcid":"https://orcid.org/0000-0003-0189-5355"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qing-Wen Wang","raw_affiliation_strings":["Collaborative Innovation Center for the Marine Artificial Intelligence, Shanghai 200444, China","Department of Mathematics, Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China"],"raw_orcid":"https://orcid.org/0000-0003-0189-5355","affiliations":[{"raw_affiliation_string":"Collaborative Innovation Center for the Marine Artificial Intelligence, Shanghai 200444, China","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics, Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113241658","display_name":"Lv-Ming Xie","orcid":null},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lv-Ming Xie","raw_affiliation_strings":["Department of Mathematics, Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China","institution_ids":["https://openalex.org/I113940042"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100771668"],"corresponding_institution_ids":["https://openalex.org/I113940042"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":8.2312,"has_fulltext":true,"cited_by_count":32,"citation_normalized_percentile":{"value":0.98170447,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"16","issue":"3","first_page":"287","last_page":"287"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9952999949455261,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9458000063896179,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.8946512937545776},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.744792103767395},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.6671326160430908},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6117093563079834},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5452365279197693},{"id":"https://openalex.org/keywords/graphics","display_name":"Graphics","score":0.5187385678291321},{"id":"https://openalex.org/keywords/quaternion-algebra","display_name":"Quaternion algebra","score":0.4825248420238495},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4462965130805969},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38570746779441833},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33889371156692505},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2919098138809204},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08281716704368591},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.05666738748550415}],"concepts":[{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.8946512937545776},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.744792103767395},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.6671326160430908},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6117093563079834},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5452365279197693},{"id":"https://openalex.org/C21442007","wikidata":"https://www.wikidata.org/wiki/Q1027879","display_name":"Graphics","level":2,"score":0.5187385678291321},{"id":"https://openalex.org/C151640129","wikidata":"https://www.wikidata.org/wiki/Q2835967","display_name":"Quaternion algebra","level":5,"score":0.4825248420238495},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4462965130805969},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38570746779441833},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33889371156692505},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2919098138809204},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08281716704368591},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.05666738748550415},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"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/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C100899422","wikidata":"https://www.wikidata.org/wiki/Q5058347","display_name":"Cellular algebra","level":4,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym16030287","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16030287","pdf_url":"https://www.mdpi.com/2073-8994/16/3/287/pdf?version=1709289124","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:634239b263a84eb1a84b62dc8a826c50","is_oa":false,"landing_page_url":"https://doaj.org/article/634239b263a84eb1a84b62dc8a826c50","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 16, Iss 3, p 287 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym16030287","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16030287","pdf_url":"https://www.mdpi.com/2073-8994/16/3/287/pdf?version=1709289124","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7068616604","display_name":null,"funder_award_id":"12371023","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4392386288.pdf"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1599279268","https://openalex.org/W1971734187","https://openalex.org/W1990902077","https://openalex.org/W2000234192","https://openalex.org/W2012683663","https://openalex.org/W2043712519","https://openalex.org/W2073632201","https://openalex.org/W2077609945","https://openalex.org/W2082674017","https://openalex.org/W2086055091","https://openalex.org/W2088350304","https://openalex.org/W2092942375","https://openalex.org/W2114765937","https://openalex.org/W2138455274","https://openalex.org/W2145229729","https://openalex.org/W2221636542","https://openalex.org/W2388888330","https://openalex.org/W2604559994","https://openalex.org/W2948251984","https://openalex.org/W2994810017","https://openalex.org/W3101831395","https://openalex.org/W3102718792","https://openalex.org/W3184923368","https://openalex.org/W3214066271","https://openalex.org/W4212977886","https://openalex.org/W4300605813","https://openalex.org/W4372218710","https://openalex.org/W6736490045"],"related_works":["https://openalex.org/W2058788062","https://openalex.org/W4362700167","https://openalex.org/W775106713","https://openalex.org/W2949247699","https://openalex.org/W2377268185","https://openalex.org/W2946572075","https://openalex.org/W4291249731","https://openalex.org/W2749494690","https://openalex.org/W2962847582","https://openalex.org/W4213061425"],"abstract_inverted_index":{"Dual":[0],"quaternions":[1],"have":[2],"wide":[3],"applications":[4],"in":[5,17],"automatic":[6],"differentiation,":[7],"computer":[8],"graphics,":[9],"mechanics,":[10],"and":[11,49,61,95],"others.":[12],"Due":[13],"to":[14,103],"its":[15],"application":[16],"control":[18],"theory,":[19],"matrix":[20,34,58,84],"equation":[21,35,59,85],"AXB=C":[22,36],"has":[23],"been":[24],"extensively":[25],"studied.":[26],"However,":[27],"there":[28],"is":[29,71],"currently":[30],"limited":[31],"information":[32],"on":[33],"regarding":[37],"the":[38,47,53,63,66,78,88,91,105],"dual":[39,56,82],"quaternion":[40,57,83],"algebra.":[41],"In":[42],"this":[43,110],"paper,":[44],"we":[45,76,98],"provide":[46],"necessary":[48],"sufficient":[50],"conditions":[51],"for":[52,65,81],"solvability":[54],"of":[55,93,109],"AXB=C,":[60],"present":[62,99],"expression":[64],"general":[67],"solution":[68],"when":[69],"it":[70],"solvable.":[72],"As":[73],"an":[74],"application,":[75],"derive":[77],"\u03d5-Hermitian":[79,89],"solutions":[80],"AXA\u03d5=C,":[86],"where":[87],"extends":[90],"concepts":[92],"Hermiticity":[94],"\u03b7-Hermiticity.":[96],"Lastly,":[97],"a":[100],"numerical":[101],"example":[102],"verify":[104],"main":[106],"research":[107],"results":[108],"paper.":[111]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":15}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}