{"id":"https://openalex.org/W2162816170","doi":null,"title":"EXTREME POINTS RELATED TO MATRIX ALGEBRAS","display_name":"EXTREME POINTS RELATED TO MATRIX ALGEBRAS","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2162816170","mag":"2162816170"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.571.772","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.571.772","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://kkms.kangwon.ac.kr/kkms/vol09_1/09105.pdf","raw_type":"text"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5029365493","display_name":"Tae Keug Lee","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tae Keug Lee","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5029365493"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":95},"biblio":{"volume":"9","issue":"1","first_page":"45","last_page":"52"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.98580002784729,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.98580002784729,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11545","display_name":"Advanced Banach Space Theory","score":0.004800000227987766,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.0010999999940395355,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/extreme-points","display_name":"extreme points","score":0.9710000157356262},{"id":"https://openalex.org/keywords/matrix-algebra","display_name":"matrix algebra","score":0.9660000205039978},{"id":"https://openalex.org/keywords/pure-states","display_name":"pure states","score":0.9990000128746033},{"id":"https://openalex.org/keywords/positive-semidefinite-matrices","display_name":"positive semidefinite matrices","score":0.6549999713897705},{"id":"https://openalex.org/keywords/bijections","display_name":"bijections","score":0.8849999904632568}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8260455131530762},{"id":"https://openalex.org/C39847760","wikidata":"https://www.wikidata.org/wiki/Q1385465","display_name":"Extreme point","level":2,"score":0.7795711755752563},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6972585320472717},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.6774963140487671},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5832918882369995},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5294964909553528},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36512327194213867},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08062994480133057},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.06525266170501709},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.571.772","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.571.772","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://kkms.kangwon.ac.kr/kkms/vol09_1/09105.pdf","raw_type":"text"},{"id":"mag:2162816170","doi":null,"is_oa":false,"landing_page_url":"http://www.koreascience.or.kr/article/ArticleFullRecord.jsp?cn=E1KKMK_2001_v9n1_45","pdf_url":null,"source":{"id":"https://openalex.org/S2764687798","display_name":"Korean Journal of Mathematics","issn_l":"1976-8605","issn":["1976-8605","2288-1433"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-c","kci-registered","poland-20","russia-white-list-3"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Korean Journal of Mathematics","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1586975367","https://openalex.org/W2014246402","https://openalex.org/W2116102644","https://openalex.org/W2588911661","https://openalex.org/W3126588943"],"related_works":["https://openalex.org/W2962790078","https://openalex.org/W2110572285","https://openalex.org/W4405433447","https://openalex.org/W2018833859","https://openalex.org/W2014061977","https://openalex.org/W2026820086","https://openalex.org/W2023706405","https://openalex.org/W1974145659","https://openalex.org/W2546705440","https://openalex.org/W2016708525"],"abstract_inverted_index":{"Abstract.":[0],"Let":[1],"A":[2,41,53],"denote":[3],"the":[4,16,25,46],"set":[5,17,26,47],"{a":[6],"\u2208":[7],"Mn":[8],"\u2223\u2223a":[9],"\u2265":[10],"0,":[11],"tr(a)":[12],"=":[13],"1},":[14],"St(Mn)":[15],"of":[18,27,48,52],"all":[19,28,49],"states":[20,30],"on":[21,31,66,80],"Mn,":[22],"and":[23,42,44,54,60],"PS(Mn)":[24],"pure":[29,78],"Mn.":[32],"We":[33,56],"show":[34],"that":[35],"there":[36],"are":[37],"one-to-one":[38],"correspon-dences":[39],"between":[40,45],"St(Mn),":[43],"extreme":[50],"points":[51],"PS(Mn).":[55],"find":[57],"a":[58,64,77],"necessary":[59],"sufficient":[61],"condi-tion":[62],"for":[63],"state":[65,79],"Mn1":[67],"\u2295":[68],"\u00b7":[69,70,71],"\u2295Mnk":[72],"to":[73,76],"be":[74],"extended":[75],"Mn1+\u00b7\u00b7\u00b7+nk.":[81]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2016-06-24T00:00:00"}