{"id":"https://openalex.org/W2056807975","doi":"https://doi.org/10.1137/s0895479894266568","title":"Principal Submatrices, Geometric Multiplicities, and Structured Eigenvectors","display_name":"Principal Submatrices, Geometric Multiplicities, and Structured Eigenvectors","publication_year":1995,"publication_date":"1995-07-01","ids":{"openalex":"https://openalex.org/W2056807975","doi":"https://doi.org/10.1137/s0895479894266568","mag":"2056807975"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479894266568","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479894266568","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/A5111066366","display_name":"Charles R. Johnson","orcid":"https://orcid.org/0000-0001-8707-8596"},"institutions":[{"id":"https://openalex.org/I4210136924","display_name":"Colonial Williamsburg Foundation","ror":"https://ror.org/03w0tq079","country_code":"US","type":"archive","lineage":["https://openalex.org/I4210136924"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Charles R. Johnson","raw_affiliation_strings":["Williamsburg, Virginia 23187-8795"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Williamsburg, Virginia 23187-8795","institution_ids":["https://openalex.org/I4210136924"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060157911","display_name":"Brenda K. Kroschel","orcid":null},"institutions":[{"id":"https://openalex.org/I4210136924","display_name":"Colonial Williamsburg Foundation","ror":"https://ror.org/03w0tq079","country_code":"US","type":"archive","lineage":["https://openalex.org/I4210136924"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Brenda K. Kroschel","raw_affiliation_strings":["Williamsburg, Virginia 23187-8795"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Williamsburg, Virginia 23187-8795","institution_ids":["https://openalex.org/I4210136924"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210136924"],"apc_list":null,"apc_paid":null,"fwci":1.046,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.76415598,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"16","issue":"3","first_page":"1004","last_page":"1012"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9836999773979187,"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":0.9718000292778015,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.8235162496566772},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8231085538864136},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.8049604892730713},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.7341444492340088},{"id":"https://openalex.org/keywords/interlacing","display_name":"Interlacing","score":0.5845398902893066},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.5433024764060974},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5164368748664856},{"id":"https://openalex.org/keywords/converse","display_name":"Converse","score":0.5073778033256531},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4777918756008148},{"id":"https://openalex.org/keywords/divide-and-conquer-eigenvalue-algorithm","display_name":"Divide-and-conquer eigenvalue algorithm","score":0.44853267073631287},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4037032127380371},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33957648277282715},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10906293988227844}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.8235162496566772},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8231085538864136},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.8049604892730713},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.7341444492340088},{"id":"https://openalex.org/C95439218","wikidata":"https://www.wikidata.org/wiki/Q1666173","display_name":"Interlacing","level":2,"score":0.5845398902893066},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.5433024764060974},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5164368748664856},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.5073778033256531},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4777918756008148},{"id":"https://openalex.org/C192702615","wikidata":"https://www.wikidata.org/wiki/Q5283998","display_name":"Divide-and-conquer eigenvalue algorithm","level":3,"score":0.44853267073631287},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4037032127380371},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33957648277282715},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10906293988227844},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer 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/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0895479894266568","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479894266568","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:oai:ir.stthomas.edu:cas_mathpub-1167","is_oa":false,"landing_page_url":"https://ir.stthomas.edu/cas_mathpub/168","pdf_url":null,"source":{"id":"https://openalex.org/S4377196573","display_name":"UST Research Online (University of St. Thomas - Minnesota)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I161515732","host_organization_name":"University of St. Thomas - Minnesota","host_organization_lineage":["https://openalex.org/I161515732"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics Faculty Publications & Data","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.5400000214576721,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1966855976","https://openalex.org/W2094456115","https://openalex.org/W2145713479","https://openalex.org/W2146719994","https://openalex.org/W2040464292","https://openalex.org/W1971548948","https://openalex.org/W1967504793","https://openalex.org/W2014406936","https://openalex.org/W1980921095","https://openalex.org/W1993283237"],"abstract_inverted_index":{"It":[0],"is":[1,10,35,57,60],"a":[2],"straightforward":[3],"matrix":[4],"calculation":[5],"that":[6,44,59],"if":[7],"$\\lambda":[8,33],"$":[9,21,34],"an":[11,16,37],"eigenvalue":[12,38,111],"of":[13,24,39,42,67,94,107],"A,":[14],"x":[15,28],"associated":[17],"eigenvector":[18],"and":[19,49,83,103],"$\\alpha":[20,53],"the":[22,40,47,61,68,78,92,97,105,108],"set":[23],"positions":[25],"in":[26,46,65,96,113],"which":[27],"has":[29],"nonzero":[30],"entries,":[31],"then":[32],"also":[36],"submatrix":[41],"A":[43,55],"lies":[45],"rows":[48],"columns":[50],"indexed":[51],"by":[52,76],"$.":[54],"converse":[56],"presented":[58],"most":[62],"general":[63],"possible":[64],"terms":[66],"data":[69],"we":[70],"use.":[71],"Several":[72],"corollaries":[73,87],"are":[74],"obtained":[75],"applying":[77],"main":[79],"result":[80],"to":[81,89,104],"normal":[82],"Hermitian":[84,101],"matrices.":[85],"These":[86],"lead":[88],"results":[90],"concerning":[91],"case":[93],"equality":[95],"interlacing":[98],"inequalities":[99],"for":[100],"matrices,":[102],"problem":[106],"relationship":[109],"among":[110],"multiplicities":[112],"various":[114],"principal":[115],"submatrices.":[116]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}