{"id":"https://openalex.org/W2047595618","doi":"https://doi.org/10.1137/s0895479895273608","title":"On Eigenvalues of Quadratic Matrix Polynomials and Their Perturbations","display_name":"On Eigenvalues of Quadratic Matrix Polynomials and Their Perturbations","publication_year":1996,"publication_date":"1996-07-01","ids":{"openalex":"https://openalex.org/W2047595618","doi":"https://doi.org/10.1137/s0895479895273608","mag":"2047595618"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479895273608","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479895273608","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/A5008056498","display_name":"M. Radjabalipour","orcid":"https://orcid.org/0000-0003-4996-2780"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"M. Radjabalipour","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5002422251","display_name":"Abbas Salemi","orcid":"https://orcid.org/0000-0002-9403-2550"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. Salemi","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5008056498"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.17518948,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"17","issue":"3","first_page":"563","last_page":"569"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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/T11476","display_name":"Graph theory and applications","score":0.9891999959945679,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9868999719619751,"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":0.8461199998855591},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.8421998023986816},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6161394715309143},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.5666015148162842},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.512535572052002},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5028733611106873},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.4916754364967346},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.45932647585868835},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.44206273555755615},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.41812068223953247},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29037249088287354},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28702545166015625}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8461199998855591},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.8421998023986816},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6161394715309143},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.5666015148162842},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.512535572052002},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5028733611106873},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.4916754364967346},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.45932647585868835},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.44206273555755615},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.41812068223953247},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29037249088287354},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28702545166015625},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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/s0895479895273608","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479895273608","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":4,"referenced_works":["https://openalex.org/W597403463","https://openalex.org/W2000031927","https://openalex.org/W2010795374","https://openalex.org/W2084223413"],"related_works":["https://openalex.org/W3196977684","https://openalex.org/W4230581126","https://openalex.org/W4317464059","https://openalex.org/W2951695430","https://openalex.org/W4378765297","https://openalex.org/W4378757502","https://openalex.org/W4385248177","https://openalex.org/W2994793674","https://openalex.org/W2761548024","https://openalex.org/W2077036309"],"abstract_inverted_index":{"Following":[0],"the":[1,9,13,20,23,56,61,71,99,103,107,131],"terminology":[2],"used":[3],"by":[4],"Gohberg,":[5],"Lancaster,":[6],"and":[7,51,95],"Rodman,":[8],"main":[10],"results":[11],"of":[12,22,26,60,106,113,134],"paper":[14],"are":[15],"as":[16],"follows.":[17],"(i)":[18],"Studying":[19],"values":[21],"partial":[24],"multiplicities":[25],"a":[27,129],"matrix":[28],"polynomial":[29,73],"$A(":[30],"\\lambda":[31,34,38,64,66,76,82,85,115],")":[32,78,83,117],"=":[33,79,118],"^2":[35],"I":[36],"+":[37,40,84],"C":[39,94],"K$":[41],"with":[42],"hermitian":[43],"coefficients":[44],"at":[45],"real":[46],"eigenvalues":[47],"$\\lambda":[48,109,121,135],"_0":[49,67,122,136],"$":[50,69,123],"determining":[52],"sharp":[53],"bounds":[54],"for":[55],"highest":[57],"degree":[58],"d":[59],"factor":[62],"$(":[63],"-":[65],")^d":[68],"in":[70,102],"bivariate":[72],"$t":[74],"(":[75,81,110],",\\epsilon":[77,116],"\\det(A":[80],"\\in":[86],"C)$.":[87],"(ii)":[88],"Finding":[89],"conditions":[90],"on":[91],"general":[92],"matrices":[93],"K":[96],"implying":[97],"that":[98],"leading":[100],"exponent":[101],"Puiseux":[104],"expansion":[105],"zero":[108],"\\epsilon":[111],")$":[112],"$t(":[114],"0$":[119],"near":[120],"is":[124,130],"$1":[125],"/":[126],"a$,":[127],"where":[128],"algebraic":[132],"multiplicity":[133],"$.":[137]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
