{"id":"https://openalex.org/W2154413958","doi":"https://doi.org/10.1109/tit.1975.1055474","title":"On the minimal spectral factorization of nonsingular positive rational matrices","display_name":"On the minimal spectral factorization of nonsingular positive rational matrices","publication_year":1975,"publication_date":"1975-11-01","ids":{"openalex":"https://openalex.org/W2154413958","doi":"https://doi.org/10.1109/tit.1975.1055474","mag":"2154413958"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1975.1055474","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1975.1055474","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","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/A5022355148","display_name":"Joos Vandewalle","orcid":"https://orcid.org/0000-0001-7716-2460"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"J. Vandewalle","raw_affiliation_strings":["Laboratory for Networks and Systems, Katholieke Universiteit Leuven, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory for Networks and Systems, Katholieke Universiteit Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035921496","display_name":"P. Dewilde","orcid":"https://orcid.org/0000-0002-9553-1845"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"P. Dewilde","raw_affiliation_strings":["Laboratory for Networks and Systems, Katholieke Universiteit Leuven, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory for Networks and Systems, Katholieke Universiteit Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":null,"apc_paid":null,"fwci":2.7749,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.92739884,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"21","issue":"6","first_page":"612","last_page":"618"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9850999712944031,"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":0.9850999712944031,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.7736572027206421},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.7166831493377686},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6864316463470459},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.570630669593811},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.5075210332870483},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.4876035749912262},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.47337764501571655},{"id":"https://openalex.org/keywords/spectral-theorem","display_name":"Spectral theorem","score":0.4732166826725006},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3933345079421997},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36129701137542725},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3378744125366211},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2884451746940613},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.1666664183139801},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0946313738822937}],"concepts":[{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.7736572027206421},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.7166831493377686},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6864316463470459},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.570630669593811},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.5075210332870483},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.4876035749912262},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.47337764501571655},{"id":"https://openalex.org/C35958075","wikidata":"https://www.wikidata.org/wiki/Q1425077","display_name":"Spectral theorem","level":3,"score":0.4732166826725006},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3933345079421997},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36129701137542725},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3378744125366211},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2884451746940613},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.1666664183139801},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0946313738822937},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1975.1055474","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1975.1055474","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W330372241","https://openalex.org/W1963502260","https://openalex.org/W1995590150","https://openalex.org/W2006110459","https://openalex.org/W2030585053","https://openalex.org/W2044578857","https://openalex.org/W2077950830","https://openalex.org/W2128978199","https://openalex.org/W2132658950","https://openalex.org/W2163101083","https://openalex.org/W3049314758"],"related_works":["https://openalex.org/W2013504776","https://openalex.org/W2012515769","https://openalex.org/W2132739882","https://openalex.org/W3041423264","https://openalex.org/W4287165289","https://openalex.org/W3170626941","https://openalex.org/W1979383835","https://openalex.org/W119752240","https://openalex.org/W2120310025","https://openalex.org/W4287265791"],"abstract_inverted_index":{"In":[0],"this":[1,73],"paper":[2],"a":[3,17,23,56,89,120],"novel":[4],"theory":[5],"and":[6,59,122],"algorithm":[7,79],"for":[8,19],"spectral":[9,82,100],"factorization":[10,90,101],"is":[11,14,105,114],"presented.":[12],"It":[13],"based":[15],"on":[16],"criterion":[18],"minimal":[20,124],"extraction":[21],"of":[22,64,97,103,111],"so-called":[24],"\"elementary":[25],"factor.\"":[26],"Although":[27],"not":[28],"all":[29],"positive":[30],"para-hermitian":[31],"matrices":[32],"can":[33,43],"be":[34,44],"minimally":[35],"factored":[36],"into":[37],"elementary":[38],"factors,":[39],"still":[40],"the":[41,48,53,61,67,78,81,98,109,112],"method":[42,70,113],"adapted":[45],"to":[46],"fit":[47],"general":[49],"case":[50],"by":[51],"increasing":[52],"degree":[54,65],"in":[55,72,84,119],"well-controlled":[57],"way":[58],"removing":[60],"nonminimal":[62],"units":[63],"at":[66],"end.":[68],"The":[69,116],"is,":[71],"sense,":[74],"strictly":[75],"minimal.":[76],"Moreover,":[77],"produces":[80],"factor":[83],"ali":[85],"cases":[86],"where":[87],"such":[88],"does":[91],"exist.":[92],"Also,":[93],"an":[94],"independent":[95],"proof":[96],"famous":[99],"result":[102],"Youla":[104],"obtained,":[106],"so":[107],"that":[108],"completeness":[110],"ascertained.":[115],"procedure":[117],"results":[118],"workable":[121],"optimally":[123],"algorithm.":[125]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
