{"id":"https://openalex.org/W2528399447","doi":"https://doi.org/10.1137/16m1064908","title":"Near Normal Dilations of Nonnormal Matrices and Linear Operators","display_name":"Near Normal Dilations of Nonnormal Matrices and Linear Operators","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2528399447","doi":"https://doi.org/10.1137/16m1064908","mag":"2528399447"},"language":"en","primary_location":{"id":"doi:10.1137/16m1064908","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1064908","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/A5019550551","display_name":"Anne Greenbaum","orcid":"https://orcid.org/0000-0002-3783-3466"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Anne Greenbaum","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023365889","display_name":"Trevor Caldwell","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Trevor Caldwell","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5048012256","display_name":"Kenan Li","orcid":"https://orcid.org/0000-0002-4641-6699"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kenan Li","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5019550551"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6969,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.75466585,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"37","issue":"4","first_page":"1365","last_page":"1381"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991000294685364,"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":0.9991000294685364,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.9970999956130981,"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"}},{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9962000250816345,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8549289107322693},{"id":"https://openalex.org/keywords/dilation","display_name":"Dilation (metric space)","score":0.7426993250846863},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6765815019607544},{"id":"https://openalex.org/keywords/operator-matrix","display_name":"Operator matrix","score":0.6098863482475281},{"id":"https://openalex.org/keywords/linear-map","display_name":"Linear map","score":0.49711039662361145},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.4672558009624481},{"id":"https://openalex.org/keywords/quasinormal-operator","display_name":"Quasinormal operator","score":0.4403068721294403},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4366753101348877},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.43199366331100464},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.42996761202812195},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3690945506095886},{"id":"https://openalex.org/keywords/finite-rank-operator","display_name":"Finite-rank operator","score":0.34167712926864624},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.1771622598171234}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8549289107322693},{"id":"https://openalex.org/C2780757906","wikidata":"https://www.wikidata.org/wiki/Q5276676","display_name":"Dilation (metric space)","level":2,"score":0.7426993250846863},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6765815019607544},{"id":"https://openalex.org/C2992500303","wikidata":"https://www.wikidata.org/wiki/Q5680845","display_name":"Operator matrix","level":2,"score":0.6098863482475281},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.49711039662361145},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.4672558009624481},{"id":"https://openalex.org/C24250787","wikidata":"https://www.wikidata.org/wiki/Q7269510","display_name":"Quasinormal operator","level":4,"score":0.4403068721294403},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4366753101348877},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43199366331100464},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.42996761202812195},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3690945506095886},{"id":"https://openalex.org/C99392333","wikidata":"https://www.wikidata.org/wiki/Q5450385","display_name":"Finite-rank operator","level":3,"score":0.34167712926864624},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.1771622598171234},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1064908","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1064908","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/G5255151525","display_name":null,"funder_award_id":"1210886","funder_id":"https://openalex.org/F4320332172","funder_display_name":"Directorate for Mathematical and Physical Sciences"}],"funders":[{"id":"https://openalex.org/F4320332172","display_name":"Directorate for Mathematical and Physical Sciences","ror":"https://ror.org/029b7h395"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W175988912","https://openalex.org/W1575147392","https://openalex.org/W1602120208","https://openalex.org/W1602420091","https://openalex.org/W1854863599","https://openalex.org/W1972703189","https://openalex.org/W1993430967","https://openalex.org/W2005916081","https://openalex.org/W2015964742","https://openalex.org/W2016761091","https://openalex.org/W2046511598","https://openalex.org/W2087373438","https://openalex.org/W2963096972","https://openalex.org/W4251579809"],"related_works":["https://openalex.org/W4308895499","https://openalex.org/W2362518496","https://openalex.org/W2013614240","https://openalex.org/W2345353395","https://openalex.org/W203872328","https://openalex.org/W767095570","https://openalex.org/W3199283680","https://openalex.org/W4285761056","https://openalex.org/W4286380433","https://openalex.org/W2044200444"],"abstract_inverted_index":{"Let":[0],"$A$":[1,19],"be":[2,60,142],"a":[3,7,11,21,26,61,68,116,201,207],"square":[4],"matrix":[5],"or":[6,67,123,211],"linear":[8,22],"operator":[9,23,115,132,140,170,198],"on":[10,25,200],"Hilbert":[12],"space":[13,28],"${\\cal":[14,29,51],"H}$.":[15,52],"A":[16],"dilation":[17,62],"of":[18,63,70,84,94,97,99,108,119,161,167,174,178,185,203],"is":[20,47,55,124,233],"$M$":[24],"larger":[27,131],"K}":[30],"\\supset":[31],"{\\cal":[32],"H}$":[33],"such":[34],"that":[35,58,107,195,209],"$A":[36],"=":[37],"\\left.":[38],"P_{{\\cal":[39],"H}}":[40],"M":[41],"\\right|_{\\cal":[42],"H}$,":[43],"where":[44,137],"$P_{{\\cal":[45],"H}}$":[46],"orthogonal":[48],"projection":[49],"onto":[50],"Often":[53],"it":[54,104,125],"required":[56],"additionally":[57],"$M^k$":[59],"$A^k$":[64],"for":[65,146,151,189],"all":[66],"range":[69,177],"positive":[71],"integer":[72],"powers":[73],"$k$.":[74],"While":[75],"much":[76],"work":[77],"has":[78,90],"been":[79,91],"aimed":[80],"at":[81],"proving":[82],"existence":[83],"dilations":[85,101,160,228],"with":[86,164],"various":[87],"properties,":[88],"there":[89],"little":[92],"study":[93],"the":[95,109,113,120,130,138,165,168,172,175,179,183,196,216,220],"behavior":[96,184,232],"functions":[98],"these":[100],"and":[102,187],"how":[103],"compares":[105],"to":[106,219],"original":[110,114,139,221],"operator.":[111,222],"Is":[112],"major":[117],"part":[118,217],"dilated":[121,169,197],"one":[122],"an":[126,143],"insignificant":[127],"piece?":[128],"Does":[129],"represent":[133],"some":[134],"physical":[135],"process,":[136],"might":[141],"important":[144],"component":[145],"certain":[147],"times":[148],"but":[149,213],"not":[150],"others?":[152],"In":[153],"this":[154,231],"paper":[155],"we":[156],"construct":[157],"near":[158,226],"normal":[159,227],"nonnormal":[162],"matrices,":[163],"spectrum":[166],"around":[171],"boundary":[173],"numerical":[176],"matrix.":[180],"We":[181,193,223],"compare":[182],"$e^{tA}$":[186],"$e^{tM}$":[188],"$t":[190],">":[191],"0$.":[192],"find":[194],"takes":[199],"life":[202],"its":[204],"own,":[205],"representing":[206],"wave":[208],"grows":[210],"decays":[212],"eventually":[214],"dominates":[215],"corresponding":[218],"derive":[224],"other":[225],"in":[229],"which":[230],"less":[234],"pronounced.":[235]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}