{"id":"https://openalex.org/W7213358262","doi":"https://doi.org/10.48550/arxiv.2609.14303","title":"Regional Stability and New Eigenvalue Perturbation Bounds","display_name":"Regional Stability and New Eigenvalue Perturbation Bounds","publication_year":2026,"publication_date":"2026-09-13","ids":{"openalex":"https://openalex.org/W7213358262","doi":"https://doi.org/10.48550/arxiv.2609.14303"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.14303","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14303","pdf_url":"https://arxiv.org/pdf/2609.14303","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.14303","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137310488","display_name":"Phuc Tran","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210142044","display_name":"VinUniversity","ror":"https://ror.org/052dmdr17","country_code":"VN","type":"education","lineage":["https://openalex.org/I4210142044"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Tran, Phuc","raw_affiliation_strings":["School of Engineering , VinUniversity"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering , VinUniversity","institution_ids":["https://openalex.org/I4210142044"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5151800880","display_name":"Van Vu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210116809","display_name":"Hong Kong Virtual University","ror":"https://ror.org/023mp3m37","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210116809"]},{"id":"https://openalex.org/I4210142044","display_name":"VinUniversity","ror":"https://ror.org/052dmdr17","country_code":"VN","type":"education","lineage":["https://openalex.org/I4210142044"]},{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["CN","HK","VN"],"is_corresponding":false,"raw_author_name":"Vu, Van","raw_affiliation_strings":["Department of Mathematics , The University of Hong Kong (HKU)","School of Engineering , VinUniversity"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , The University of Hong Kong (HKU)","institution_ids":["https://openalex.org/I4210116809","https://openalex.org/I889458895"]},{"raw_affiliation_string":"School of Engineering , VinUniversity","institution_ids":["https://openalex.org/I4210142044"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9634000062942505,"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":0.9634000062942505,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.028699999675154686,"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/T11716","display_name":"Random Matrices and Applications","score":0.003599999938160181,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/symmetric-matrices","display_name":"symmetric matrices","score":0.7829999923706055},{"id":"https://openalex.org/keywords/weyl-s-inequality","display_name":"Weyl's inequality","score":0.871999979019165},{"id":"https://openalex.org/keywords/regional-stability","display_name":"regional stability","score":0.9049999713897705},{"id":"https://openalex.org/keywords/eigenvalue-stability","display_name":"eigenvalue stability","score":0.460999995470047},{"id":"https://openalex.org/keywords/stochastic-perturbation","display_name":"random perturbations","score":0.6240000128746033},{"id":"https://openalex.org/keywords/neumann-series","display_name":"Neumann series","score":0.9150000214576721},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrices","score":0.8289999961853027},{"id":"https://openalex.org/keywords/rectangular-matrices","display_name":"rectangular matrices","score":0.9100000262260437}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.795799970626831},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7674000263214111},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.6478000283241272},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.6412000060081482},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.6047000288963318},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4569999873638153},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39259999990463257},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.3894999921321869},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.3544999957084656},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3508000075817108},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.34459999203681946},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33480000495910645},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.3345000147819519},{"id":"https://openalex.org/C46865736","wikidata":"https://www.wikidata.org/wiki/Q5348914","display_name":"Eigenvalue perturbation","level":3,"score":0.3310000002384186},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.3287999927997589},{"id":"https://openalex.org/C73772418","wikidata":"https://www.wikidata.org/wiki/Q6888018","display_name":"Modal matrix","level":5,"score":0.3231000006198883},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.28790000081062317},{"id":"https://openalex.org/C143170015","wikidata":"https://www.wikidata.org/wiki/Q17007850","display_name":"Stability conditions","level":3,"score":0.2506999969482422}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.14303","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14303","pdf_url":"https://arxiv.org/pdf/2609.14303","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.14303","doi":"https://doi.org/10.48550/arxiv.2609.14303","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.14303","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.14303","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14303","pdf_url":"https://arxiv.org/pdf/2609.14303","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213358262.pdf","grobid_xml":"https://content.openalex.org/works/W7213358262.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7075353210","https://openalex.org/W2331698088","https://openalex.org/W7214574391","https://openalex.org/W7140128917","https://openalex.org/W2486480483","https://openalex.org/W2320978172","https://openalex.org/W7214797328","https://openalex.org/W2358110654","https://openalex.org/W2791583265","https://openalex.org/W2019227726"],"abstract_inverted_index":{"Let":[0,11],"$A$":[1],"be":[2,132,174],"an":[3],"$n\\times":[4],"n$":[5],"symmetric":[6,18],"matrix":[7],"with":[8,76],"eigenvalues":[9,24],"$\u03bb_1\\geq\\cdots\\geq\u03bb_n$.":[10],"$\\tilde":[12,26],"A:=A+E$,":[13],"where":[14,70],"$E$":[15,61,71,84],"is":[16,37,85,145,165,170],"a":[17,38,89,115,121,125],"noise":[19],"matrix,":[20],"and":[21,44,62,104,172],"denote":[22],"the":[23,31,57,63,68,102,109,128,135,141,166],"of":[25,65,114,138,146],"A$":[27],"by":[28,55],"$\\tilde\u03bb_1\\geq\\cdots\\geq\\tilde\u03bb_n$.":[29],"Bounding":[30],"perturbation":[32,53],"$|\\tilde":[33],"\u03bb_i":[34],"-\u03bb_i|":[35],"$":[36],"central":[39],"problem":[40],"in":[41,176],"linear":[42],"algebra":[43],"numerical":[45],"analysis.":[46,158],"In":[47,67],"this":[48],"paper,":[49],"we":[50,87],"prove":[51,150],"new":[52,110,161],"results":[54,100],"exploring":[56],"actual":[58],"interaction":[59],"between":[60],"eigenvectors":[64],"$A$.":[66],"setting":[69],"does":[72],"not":[73],"act":[74],"adversarially":[75],"respect":[77],"to":[78,101,131],"these":[79,99],"vectors":[80],"(for":[81],"instance,":[82],"if":[83],"random),":[86],"obtain":[88,108],"considerable":[90],"improvement":[91],"over":[92],"Weyl's":[93],"inequality.":[94],"One":[95],"can":[96],"routinely":[97],"extend":[98],"Hermitian":[103],"rectangular":[105],"settings.":[106],"We":[107,149],"bounds":[111],"as":[112],"corollaries":[113],"regional":[116,152],"stability":[117,153],"result,":[118],"which":[119,169],"provides":[120],"sufficient":[122],"condition":[123],"for":[124],"region":[126],"on":[127],"real":[129],"line":[130],"stable":[133],"(containing":[134],"same":[136],"number":[137],"eigenvalues)":[139],"after":[140],"perturbation.":[142],"This":[143],"result":[144,154],"independent":[147],"interest.":[148],"our":[151],"using":[155],"contour":[156],"integral":[157],"Our":[159],"main":[160],"technical":[162],"ingredient":[163],"here":[164],"\\textit{double-jump}":[167],"argument,":[168],"robust":[171],"could":[173],"useful":[175],"many":[177],"other":[178],"situations":[179],"involving":[180],"Neumann":[181],"series.":[182]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-16T00:00:00"}
