{"id":"https://openalex.org/W2086481429","doi":"https://doi.org/10.1137/s0895479801387073","title":"Eigenvalues of Words in Two Positive Definite Letters","display_name":"Eigenvalues of Words in Two Positive Definite Letters","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2086481429","doi":"https://doi.org/10.1137/s0895479801387073","mag":"2086481429"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479801387073","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479801387073","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/A5111066366","display_name":"Charles R. Johnson","orcid":"https://orcid.org/0000-0001-8707-8596"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Charles R. Johnson","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5039959148","display_name":"Christopher J. Hillar","orcid":"https://orcid.org/0000-0001-8575-2663"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christopher J. Hillar","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111066366"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.4994,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.93223133,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"23","issue":"4","first_page":"916","last_page":"928"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9977999925613403,"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/T11567","display_name":"semigroups and automata theory","score":0.9977999925613403,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9965000152587891,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9957000017166138,"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":0.8462233543395996},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.8190697431564331},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.813545286655426},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.721069872379303},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.5756574273109436},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5605465769767761},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5051484704017639},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.426636278629303},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4050788879394531},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37676510214805603},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.33025240898132324},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08423390984535217},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.0838417112827301},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.061399996280670166},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.046256035566329956}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8462233543395996},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.8190697431564331},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.813545286655426},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.721069872379303},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5756574273109436},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5605465769767761},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5051484704017639},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.426636278629303},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4050788879394531},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37676510214805603},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.33025240898132324},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08423390984535217},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0838417112827301},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.061399996280670166},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.046256035566329956},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0895479801387073","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479801387073","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:10.1.1.182.3276","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.182.3276","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.msri.org/people/members/chillar/files/38707.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W2004538321","https://openalex.org/W2410092892","https://openalex.org/W2610857016"],"related_works":["https://openalex.org/W1529715114","https://openalex.org/W1978042415","https://openalex.org/W3038654277","https://openalex.org/W4327724964","https://openalex.org/W3119737209","https://openalex.org/W2122837848","https://openalex.org/W2120826334","https://openalex.org/W2966383146","https://openalex.org/W3026358768","https://openalex.org/W2897153210"],"abstract_inverted_index":{"The":[0],"question":[1,22,67],"of":[2,40,70],"whether":[3],"all":[4],"words":[5,41,60],"in":[6,28,34],"two":[7],"real":[8],"positive":[9,14,45],"definite":[10],"letters":[11],"have":[12],"only":[13],"eigenvalues":[15,46],"is":[16,47,52,74],"addressed":[17],"and":[18,49],"settled":[19],"(negatively).":[20],"This":[21],"was":[23],"raised":[24],"some":[25],"time":[26],"ago":[27],"connection":[29],"with":[30],"a":[31,65],"long-standing":[32],"problem":[33],"theoretical":[35],"physics.":[36],"A":[37],"large":[38],"class":[39],"that":[42,57],"do":[43],"guarantee":[44],"identified,":[48],"considerable":[50],"evidence":[51],"given":[53],"for":[54],"the":[55,63],"conjecture":[56],"no":[58],"other":[59],"do.":[61],"In":[62],"process,":[64],"fundamental":[66],"about":[68],"solvability":[69],"symmetric":[71],"word":[72],"equations":[73],"encountered.":[75]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}