{"id":"https://openalex.org/W2041343677","doi":"https://doi.org/10.1137/s0895479892243237","title":"Variation of the Unitary Part of a Matrix","display_name":"Variation of the Unitary Part of a Matrix","publication_year":1994,"publication_date":"1994-07-01","ids":{"openalex":"https://openalex.org/W2041343677","doi":"https://doi.org/10.1137/s0895479892243237","mag":"2041343677"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479892243237","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479892243237","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/A5103094159","display_name":"Rajendra Bhatia","orcid":"https://orcid.org/0000-0002-1959-0691"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rajendra Bhatia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5029408777","display_name":"Kalyan K. Mukherjea","orcid":"https://orcid.org/0000-0002-3319-2112"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kalyan Mukherjea","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.858,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.85929596,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"15","issue":"3","first_page":"1007","last_page":"1014"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9977999925613403,"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":0.9977999925613403,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9805999994277954,"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/T11130","display_name":"Coding theory and cryptography","score":0.9502999782562256,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/mathematics","display_name":"Mathematics","score":0.7954151630401611},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.7215642929077148},{"id":"https://openalex.org/keywords/polar-decomposition","display_name":"Polar decomposition","score":0.6960267424583435},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.693483293056488},{"id":"https://openalex.org/keywords/unitary-matrix","display_name":"Unitary matrix","score":0.6816483736038208},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.6126335859298706},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.5626093149185181},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4660908281803131},{"id":"https://openalex.org/keywords/unitary-transformation","display_name":"Unitary transformation","score":0.441869854927063},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.43102771043777466},{"id":"https://openalex.org/keywords/lu-decomposition","display_name":"LU decomposition","score":0.41410452127456665},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.39391177892684937},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3668612837791443},{"id":"https://openalex.org/keywords/polar","display_name":"Polar","score":0.313987672328949},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.08515691757202148},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07011044025421143},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.06610438227653503}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7954151630401611},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.7215642929077148},{"id":"https://openalex.org/C130956294","wikidata":"https://www.wikidata.org/wiki/Q2101158","display_name":"Polar decomposition","level":3,"score":0.6960267424583435},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.693483293056488},{"id":"https://openalex.org/C96214315","wikidata":"https://www.wikidata.org/wiki/Q727103","display_name":"Unitary matrix","level":3,"score":0.6816483736038208},{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.6126335859298706},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.5626093149185181},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4660908281803131},{"id":"https://openalex.org/C179371143","wikidata":"https://www.wikidata.org/wiki/Q2495534","display_name":"Unitary transformation","level":3,"score":0.441869854927063},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.43102771043777466},{"id":"https://openalex.org/C123213974","wikidata":"https://www.wikidata.org/wiki/Q833089","display_name":"LU decomposition","level":4,"score":0.41410452127456665},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39391177892684937},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3668612837791443},{"id":"https://openalex.org/C29705727","wikidata":"https://www.wikidata.org/wiki/Q294562","display_name":"Polar","level":2,"score":0.313987672328949},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.08515691757202148},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07011044025421143},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.06610438227653503},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895479892243237","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479892243237","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":17,"referenced_works":["https://openalex.org/W125915750","https://openalex.org/W1551205560","https://openalex.org/W1965922532","https://openalex.org/W2005631662","https://openalex.org/W2034338302","https://openalex.org/W2043345643","https://openalex.org/W2051452993","https://openalex.org/W2054785041","https://openalex.org/W2055253659","https://openalex.org/W2056624349","https://openalex.org/W2057970132","https://openalex.org/W2062780857","https://openalex.org/W2065334221","https://openalex.org/W2151192928","https://openalex.org/W2152122625","https://openalex.org/W2948315098","https://openalex.org/W4212938248"],"related_works":["https://openalex.org/W2142486491","https://openalex.org/W1554154635","https://openalex.org/W1967378991","https://openalex.org/W2285133860","https://openalex.org/W2391999311","https://openalex.org/W2919544312","https://openalex.org/W2953323116","https://openalex.org/W2803115322","https://openalex.org/W2618775558","https://openalex.org/W3009839343"],"abstract_inverted_index":{"The":[0,25],"derivative":[1],"of":[2,58],"the":[3,12,17,30,36,41,59],"map":[4,31],"that":[5,32],"takes":[6,33],"an":[7],"invertible":[8],"matrix":[9],"A":[10,34],"to":[11,35,50],"unitary":[13,37],"factor":[14,38],"U":[15],"in":[16,40],"polar":[18],"decomposition":[19,43],"$A":[20,44],"=":[21,45],"UP$":[22],"is":[23,27],"evaluated.":[24],"same":[26],"done":[28],"for":[29,53],"Q":[39],"QR":[42],"QR$.":[46],"These":[47],"results":[48],"lead":[49],"perturbation":[51],"bounds":[52],"these":[54],"maps.":[55],"Other":[56],"applications":[57],"method":[60],"developed":[61],"are":[62],"discussed.":[63]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
