{"id":"https://openalex.org/W2091077216","doi":"https://doi.org/10.1137/130904624","title":"Nonpositive Eigenvalues of Hollow, Symmetric, Nonnegative Matrices","display_name":"Nonpositive Eigenvalues of Hollow, Symmetric, Nonnegative Matrices","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2091077216","doi":"https://doi.org/10.1137/130904624","mag":"2091077216"},"language":"en","primary_location":{"id":"doi:10.1137/130904624","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130904624","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/A5034877995","display_name":"Zachary Charles","orcid":"https://orcid.org/0000-0001-8997-874X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zachary B. Charles","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011248578","display_name":"Miriam Farber","orcid":"https://orcid.org/0000-0002-6729-116X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Miriam Farber","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111066366","display_name":"Charles R. Johnson","orcid":"https://orcid.org/0000-0001-8707-8596"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Charles R. Johnson","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5037125462","display_name":"Lee Kennedy\u2010Shaffer","orcid":"https://orcid.org/0000-0001-7604-3638"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lee Kennedy-Shaffer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3152,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.79914092,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"34","issue":"3","first_page":"1384","last_page":"1400"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11476","display_name":"Graph theory and applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10849","display_name":"Finite Group Theory Research","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.9987999796867371,"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/mathematics","display_name":"Mathematics","score":0.8447467684745789},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.8020716905593872},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7506327629089355},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.6705267429351807},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5425094366073608},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.5347349643707275},{"id":"https://openalex.org/keywords/main-diagonal","display_name":"Main diagonal","score":0.4958263337612152},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4470217823982239},{"id":"https://openalex.org/keywords/diagonal-matrix","display_name":"Diagonal matrix","score":0.42915087938308716},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15634611248970032},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0744265615940094}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8447467684745789},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.8020716905593872},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7506327629089355},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.6705267429351807},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5425094366073608},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.5347349643707275},{"id":"https://openalex.org/C60761296","wikidata":"https://www.wikidata.org/wiki/Q651480","display_name":"Main diagonal","level":3,"score":0.4958263337612152},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4470217823982239},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.42915087938308716},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15634611248970032},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0744265615940094},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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:10.1137/130904624","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130904624","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W326579219","https://openalex.org/W1494380125","https://openalex.org/W1500921805","https://openalex.org/W1573672270","https://openalex.org/W1589331344","https://openalex.org/W1969668722","https://openalex.org/W2037142574","https://openalex.org/W2044330456","https://openalex.org/W2048610647","https://openalex.org/W2068279164","https://openalex.org/W2089247135","https://openalex.org/W2092652179","https://openalex.org/W2095689360","https://openalex.org/W2098120084","https://openalex.org/W2144514070","https://openalex.org/W2151417892","https://openalex.org/W2154864636","https://openalex.org/W2320846818","https://openalex.org/W2401610261","https://openalex.org/W2610857016","https://openalex.org/W3149604617"],"related_works":["https://openalex.org/W2950949038","https://openalex.org/W1671489304","https://openalex.org/W2394163158","https://openalex.org/W2034598826","https://openalex.org/W2070323717","https://openalex.org/W2924468784","https://openalex.org/W3215548671","https://openalex.org/W4285317199","https://openalex.org/W1994102083","https://openalex.org/W1968644351"],"abstract_inverted_index":{"Among":[0],"hollow,":[1,55,87],"symmetric":[2],"$n$-by-$n$":[3,54,86],"nonnegative":[4,57,89],"matrices,":[5],"it":[6],"is":[7,19,37,79],"shown":[8],"that":[9],"any":[10],"number":[11,42,49,143],"$k$,":[12],"$2\\leq":[13],"k\\leq":[14],"n-1$":[15],"of":[16,27,43,50,70,119,130,136,144],"nonpositive":[17,28,51,98],"eigenvalues":[18,29,52,99],"possible.":[20],"However,":[21],"as":[22,107],"$n$":[23],"grows,":[24],"small":[25],"numbers":[26],"become":[30],"increasingly":[31],"rare.":[32],"In":[33],"particular,":[34],"if":[35,66],"there":[36],"only":[38],"a":[39,108,145],"given":[40],"finite":[41],"distinct":[44],"off-diagonal":[45,74,93,121],"entries,":[46],"the":[47,68,71,77,117,141],"minimum":[48],"(among":[53],"symmetric,":[56,88],"matrices)":[58],"grows":[59],"with":[60,91,96],"$n$,":[61],"and":[62,95],"this":[63],"remains":[64],"so":[65],"just":[67],"ratio":[69],"smallest":[72],"positive":[73,92,120],"entry":[75],"to":[76,140],"largest":[78],"bounded":[80],"away":[81],"from":[82],"zero.":[83],"Nonetheless,":[84],"every":[85],"matrix":[90],"entries":[94],"two":[97],"may":[100,134],"be":[101,135],"embedded":[102],"in":[103],"an":[104],"$(n+1)$-by-$(n+1)$":[105],"one":[106],"principal":[109],"submatrix.":[110],"This":[111],"statement":[112],"does":[113],"not":[114],"hold":[115],"without":[116],"requirement":[118],"entries.":[122],"Our":[123],"proof":[124],"recognizes":[125],"some":[126],"special,":[127],"anti-Morishima":[128],"structure":[129],"Schur":[131],"complements":[132],"which":[133],"independent":[137],"interest.":[138],"Relations":[139],"independence":[142],"graph":[146],"are":[147],"also":[148],"presented.":[149]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}