{"id":"https://openalex.org/W1976962893","doi":"https://doi.org/10.1137/0617031","title":"On the Facial Structure of the Set of Correlation Matrices","display_name":"On the Facial Structure of the Set of Correlation Matrices","publication_year":1996,"publication_date":"1996-07-01","ids":{"openalex":"https://openalex.org/W1976962893","doi":"https://doi.org/10.1137/0617031","mag":"1976962893"},"language":"en","primary_location":{"id":"doi:10.1137/0617031","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0617031","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/A5047819350","display_name":"Monique Laurent","orcid":"https://orcid.org/0000-0001-8474-2121"},"institutions":[{"id":"https://openalex.org/I2799600557","display_name":"Japan External Trade Organization","ror":"https://ror.org/0480zh114","country_code":"JP","type":"government","lineage":["https://openalex.org/I1287223417","https://openalex.org/I2799600557"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Monique Laurent","raw_affiliation_strings":["External Organisation"],"affiliations":[{"raw_affiliation_string":"External Organisation","institution_ids":["https://openalex.org/I2799600557"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108397775","display_name":"Svatopluk Poljak","orcid":null},"institutions":[{"id":"https://openalex.org/I4210148356","display_name":"GGD Amsterdam","ror":"https://ror.org/04gbbq803","country_code":"NL","type":"healthcare","lineage":["https://openalex.org/I4210088893","https://openalex.org/I4210148356"]},{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Svatopluk Poljak","raw_affiliation_strings":["P.O. Box 94079, 1090 GB Amsterdam","CWI P.O. Box 94079 1090 GB Amsterdam The Netherlands","Department of Operations Reasearch, Statistics, and System Theory BS-R9501 1995","Centrum voor Wiskunde en Informatica"],"affiliations":[{"raw_affiliation_string":"P.O. Box 94079, 1090 GB Amsterdam","institution_ids":["https://openalex.org/I4210148356"]},{"raw_affiliation_string":"CWI P.O. Box 94079 1090 GB Amsterdam The Netherlands","institution_ids":["https://openalex.org/I1341640284"]},{"raw_affiliation_string":"Department of Operations Reasearch, Statistics, and System Theory BS-R9501 1995","institution_ids":[]},{"raw_affiliation_string":"Centrum voor Wiskunde en Informatica","institution_ids":["https://openalex.org/I1341640284"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5047819350"],"corresponding_institution_ids":["https://openalex.org/I2799600557"],"apc_list":null,"apc_paid":null,"fwci":2.1937,"has_fulltext":false,"cited_by_count":75,"citation_normalized_percentile":{"value":0.85464137,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"17","issue":"3","first_page":"530","last_page":"547"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.994700014591217,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9789999723434448,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8185678720474243},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7405627965927124},{"id":"https://openalex.org/keywords/lacunary-function","display_name":"Lacunary function","score":0.7092998027801514},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6539027690887451},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.612410843372345},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.4569677412509918},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.4429633319377899},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.28937721252441406},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15136104822158813},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.15113717317581177},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10079386830329895}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8185678720474243},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7405627965927124},{"id":"https://openalex.org/C63356602","wikidata":"https://www.wikidata.org/wiki/Q1986013","display_name":"Lacunary function","level":2,"score":0.7092998027801514},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6539027690887451},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.612410843372345},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.4569677412509918},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.4429633319377899},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28937721252441406},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15136104822158813},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.15113717317581177},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10079386830329895},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0617031","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0617031","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G629491556","display_name":null,"funder_award_id":"(NWO)","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320320885","display_name":"European Research Consortium for Informatics and Mathematics","ror":"https://ror.org/055zrhj18"},{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"},{"id":"https://openalex.org/F4320331116","display_name":"Centrum Wiskunde and Informatica","ror":"https://ror.org/00x7ekv49"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1974145659","https://openalex.org/W1995439776","https://openalex.org/W2006704773","https://openalex.org/W2011100327","https://openalex.org/W2014079391","https://openalex.org/W2016794928","https://openalex.org/W2058497129","https://openalex.org/W2062124264","https://openalex.org/W2084681714","https://openalex.org/W2086119402","https://openalex.org/W2088209486","https://openalex.org/W2111230388","https://openalex.org/W2144787788","https://openalex.org/W2156085019","https://openalex.org/W4239571640","https://openalex.org/W4240790620","https://openalex.org/W4252239484"],"related_works":["https://openalex.org/W2084232468","https://openalex.org/W2326853739","https://openalex.org/W2913511827","https://openalex.org/W1585655132","https://openalex.org/W1979687372","https://openalex.org/W2035767731","https://openalex.org/W3113268931","https://openalex.org/W1969943245","https://openalex.org/W1998038210","https://openalex.org/W2057004667"],"abstract_inverted_index":{"We":[0,91],"study":[1],"the":[2,6,16,30,52,84],"facial":[3],"structure":[4],"of":[5,12,43,54,68,86],"set":[7],"$\\mathcal{E}_{n":[8,44,61,99],"\\times":[9,45,62,88,100],"n}":[10,46,63,101],"$":[11,64,72],"correlation":[13],"matrices":[14,19],"(i.e.,":[15],"positive":[17],"semidefinite":[18],"with":[20],"diagonal":[21],"entries":[22],"equal":[23],"to":[24,71,96],"1).":[25],"In":[26],"particular,":[27],"we":[28,80],"determine":[29],"possible":[31],"dimensions":[32,56],"for":[33,39],"a":[34,40],"face,":[35,42],"as":[36,38],"well":[37],"polyhedral":[41,66],"$.":[47,76,90,102],"It":[48],"turns":[49],"out":[50],"that":[51,60],"spectrum":[53],"face":[55],"is":[57],"lacunary":[58],"and":[59],"has":[65],"faces":[67,85],"dimension":[69],"up":[70],"\\approx":[73],"\\sqrt":[74],"{2n}":[75],"As":[77],"an":[78],"application,":[79],"describe":[81],"in":[82],"detail":[83],"$\\mathcal{E}_{4":[87],"4}":[89],"also":[92],"discuss":[93],"results":[94],"related":[95],"optimization":[97],"over":[98]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
