{"id":"https://openalex.org/W2052296591","doi":"https://doi.org/10.1137/090774896","title":"\u03bc-Values and Spectral Value Sets for Linear Perturbation Classes Defined by a Scalar Product","display_name":"\u03bc-Values and Spectral Value Sets for Linear Perturbation Classes Defined by a Scalar Product","publication_year":2011,"publication_date":"2011-07-01","ids":{"openalex":"https://openalex.org/W2052296591","doi":"https://doi.org/10.1137/090774896","mag":"2052296591"},"language":"en","primary_location":{"id":"doi:10.1137/090774896","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090774896","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/A5009600305","display_name":"Michael Karow","orcid":"https://orcid.org/0000-0002-3582-1488"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Michael Karow","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5009600305"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6068,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.83257819,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"32","issue":"3","first_page":"845","last_page":"865"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9976000189781189,"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/T13234","display_name":"advanced mathematical theories","score":0.9749000072479248,"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":0.866322934627533},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.6365993618965149},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.6163492202758789},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5375221967697144},{"id":"https://openalex.org/keywords/skew","display_name":"Skew","score":0.5024430751800537},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3656345307826996},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35232192277908325},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34985893964767456},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.11493989825248718},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07337260246276855},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07283675670623779},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07208186388015747}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.866322934627533},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.6365993618965149},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6163492202758789},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5375221967697144},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.5024430751800537},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3656345307826996},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35232192277908325},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34985893964767456},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.11493989825248718},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07337260246276855},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07283675670623779},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07208186388015747},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/090774896","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090774896","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:doi:10.14279/depositonce-6548","is_oa":false,"landing_page_url":"https://depositonce.tu-berlin.de/handle/11303/7275","pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W10078005","https://openalex.org/W131014589","https://openalex.org/W149522324","https://openalex.org/W1575147392","https://openalex.org/W1579645751","https://openalex.org/W1868559974","https://openalex.org/W1971298790","https://openalex.org/W1973298267","https://openalex.org/W1990838156","https://openalex.org/W2001760418","https://openalex.org/W2006729027","https://openalex.org/W2010082976","https://openalex.org/W2024986571","https://openalex.org/W2027124517","https://openalex.org/W2029226141","https://openalex.org/W2050649877","https://openalex.org/W2076755843","https://openalex.org/W2103313140","https://openalex.org/W2109090100","https://openalex.org/W2123022662","https://openalex.org/W2139529710","https://openalex.org/W2163044500","https://openalex.org/W2296319761","https://openalex.org/W4243620103","https://openalex.org/W4248573056"],"related_works":["https://openalex.org/W2483299277","https://openalex.org/W2811007068","https://openalex.org/W2292494552","https://openalex.org/W2070850717","https://openalex.org/W3163222149","https://openalex.org/W2893488544","https://openalex.org/W2328888882","https://openalex.org/W2122337041","https://openalex.org/W4248378470","https://openalex.org/W3164354604"],"abstract_inverted_index":{"We":[0,46],"study":[1],"the":[2,5,27,41,48],"variation":[3],"of":[4,7,51,55],"spectrum":[6],"matrices":[8],"under":[9,44],"perturbations":[10,54],"which":[11],"are":[12,24],"self-":[13],"or":[14],"skew-adjoint":[15],"with":[16],"respect":[17],"to":[18,35],"a":[19,56],"scalar":[20],"product.":[21],"Computable":[22],"formulas":[23],"given":[25],"for":[26,40],"associated":[28],"-values.":[29],"The":[30],"results":[31],"can":[32],"be":[33],"used":[34],"calculate":[36],"spectral":[37],"value":[38],"sets":[39],"perturbation":[42],"classes":[43],"consideration.":[45],"discuss":[47],"special":[49],"case":[50],"complex":[52],"Hamiltonian":[53,57],"matrix":[58],"in":[59],"detail.":[60]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}