{"id":"https://openalex.org/W2090646187","doi":"https://doi.org/10.1007/s11590-008-0106-5","title":"Sufficiency of linear transformations on Euclidean Jordan algebras","display_name":"Sufficiency of linear transformations on Euclidean Jordan algebras","publication_year":2008,"publication_date":"2008-10-23","ids":{"openalex":"https://openalex.org/W2090646187","doi":"https://doi.org/10.1007/s11590-008-0106-5","mag":"2090646187"},"language":"en","primary_location":{"id":"doi:10.1007/s11590-008-0106-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-008-0106-5","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","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/A5018736649","display_name":"Qin Linxia","orcid":null},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Linxia Qin","raw_affiliation_strings":["Department of Applied Mathematics, Beijing Jiaotong University, 100044, Beijing, People\u2019s Republic of China","BeiJing Jiaotong Univ"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Beijing Jiaotong University, 100044, Beijing, People\u2019s Republic of China","institution_ids":["https://openalex.org/I21193070"]},{"raw_affiliation_string":"BeiJing Jiaotong Univ","institution_ids":["https://openalex.org/I21193070"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101991493","display_name":"Lingchen Kong","orcid":null},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]},{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA","CN"],"is_corresponding":false,"raw_author_name":"Lingchen Kong","raw_affiliation_strings":["Department of Applied Mathematics, Beijing Jiaotong University, 100044, Beijing, People\u2019s Republic of China","Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada","Beijing Jiaotong University","University of Waterloo"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Beijing Jiaotong University, 100044, Beijing, People\u2019s Republic of China","institution_ids":["https://openalex.org/I21193070"]},{"raw_affiliation_string":"Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Beijing Jiaotong University","institution_ids":["https://openalex.org/I21193070"]},{"raw_affiliation_string":"University of Waterloo","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113166766","display_name":"Jiye Han","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiye Han","raw_affiliation_strings":["Institute of Applied Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences, 100080, Beijing, People\u2019s Republic of China","Academy of Mathematics and System Science, Chinese Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences, 100080, Beijing, People\u2019s Republic of China","institution_ids":["https://openalex.org/I4210120485"]},{"raw_affiliation_string":"Academy of Mathematics and System Science, Chinese Academy of Sciences","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018736649"],"corresponding_institution_ids":["https://openalex.org/I21193070"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.6515,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.84622443,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"3","issue":"2","first_page":"265","last_page":"276"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.9926999807357788,"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/convexity","display_name":"Convexity","score":0.764008641242981},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7481456995010376},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.6986983418464661},{"id":"https://openalex.org/keywords/complementarity","display_name":"Complementarity (molecular biology)","score":0.6519408822059631},{"id":"https://openalex.org/keywords/linear-map","display_name":"Linear map","score":0.6181018948554993},{"id":"https://openalex.org/keywords/jordan-algebra","display_name":"Jordan algebra","score":0.600455641746521},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.5920236110687256},{"id":"https://openalex.org/keywords/linear-complementarity-problem","display_name":"Linear complementarity problem","score":0.49184298515319824},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.4800190031528473},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4686526656150818},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.442913681268692},{"id":"https://openalex.org/keywords/computational-intelligence","display_name":"Computational intelligence","score":0.439968466758728},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.42032352089881897},{"id":"https://openalex.org/keywords/euclidean-distance-matrix","display_name":"Euclidean distance matrix","score":0.41815873980522156},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4132375717163086},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36750125885009766},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33170148730278015},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.23600858449935913},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12855729460716248},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.1147083044052124},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0750507116317749}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.764008641242981},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7481456995010376},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.6986983418464661},{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.6519408822059631},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.6181018948554993},{"id":"https://openalex.org/C100376341","wikidata":"https://www.wikidata.org/wiki/Q649977","display_name":"Jordan algebra","level":4,"score":0.600455641746521},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5920236110687256},{"id":"https://openalex.org/C34320192","wikidata":"https://www.wikidata.org/wiki/Q783105","display_name":"Linear complementarity problem","level":3,"score":0.49184298515319824},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.4800190031528473},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4686526656150818},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.442913681268692},{"id":"https://openalex.org/C139502532","wikidata":"https://www.wikidata.org/wiki/Q1122090","display_name":"Computational intelligence","level":2,"score":0.439968466758728},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42032352089881897},{"id":"https://openalex.org/C171558263","wikidata":"https://www.wikidata.org/wiki/Q5406122","display_name":"Euclidean distance matrix","level":3,"score":0.41815873980522156},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4132375717163086},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36750125885009766},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33170148730278015},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.23600858449935913},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12855729460716248},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.1147083044052124},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0750507116317749},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11590-008-0106-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-008-0106-5","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W10800830","https://openalex.org/W372538328","https://openalex.org/W1497263314","https://openalex.org/W1543439990","https://openalex.org/W1570961610","https://openalex.org/W1601741115","https://openalex.org/W1848404892","https://openalex.org/W1970000960","https://openalex.org/W1982002079","https://openalex.org/W2000151369","https://openalex.org/W2033766167","https://openalex.org/W2041638835","https://openalex.org/W2043867882","https://openalex.org/W2071877895","https://openalex.org/W2074947226","https://openalex.org/W2119254090","https://openalex.org/W2127035138","https://openalex.org/W2141616558","https://openalex.org/W4231259595","https://openalex.org/W4249667877","https://openalex.org/W4378195498"],"related_works":["https://openalex.org/W2418839529","https://openalex.org/W2014158493","https://openalex.org/W2921896049","https://openalex.org/W2367868582","https://openalex.org/W2009170196","https://openalex.org/W2090646187","https://openalex.org/W1567071012","https://openalex.org/W4252609071","https://openalex.org/W3210451834","https://openalex.org/W4390188945"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
