{"id":"https://openalex.org/W1642716668","doi":"https://doi.org/10.1137/141002256","title":"Characterizing Real-Valued Multivariate Complex Polynomials and Their Symmetric Tensor Representations","display_name":"Characterizing Real-Valued Multivariate Complex Polynomials and Their Symmetric Tensor Representations","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W1642716668","doi":"https://doi.org/10.1137/141002256","mag":"1642716668"},"language":"en","primary_location":{"id":"doi:10.1137/141002256","is_oa":false,"landing_page_url":"https://doi.org/10.1137/141002256","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/A5086913303","display_name":"Bo Jiang","orcid":"https://orcid.org/0000-0002-8924-3185"},"institutions":[{"id":"https://openalex.org/I181679659","display_name":"Shanghai University of Finance and Economics","ror":"https://ror.org/00wtvfq62","country_code":"CN","type":"education","lineage":["https://openalex.org/I181679659"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bo Jiang","raw_affiliation_strings":["SHANGHAI UNIVERSITY OF FINANCE AND ECONOMICS"],"affiliations":[{"raw_affiliation_string":"SHANGHAI UNIVERSITY OF FINANCE AND ECONOMICS","institution_ids":["https://openalex.org/I181679659"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066016826","display_name":"Zhening Li","orcid":"https://orcid.org/0000-0002-6941-6931"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhening Li","raw_affiliation_strings":["School of Mathematics & Physics"],"affiliations":[{"raw_affiliation_string":"School of Mathematics & Physics","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089542160","display_name":"Shuzhong Zhang","orcid":"https://orcid.org/0000-0001-5838-1676"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shuzhong Zhang","raw_affiliation_strings":["University of\u00a0Minnesota"],"affiliations":[{"raw_affiliation_string":"University of\u00a0Minnesota","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5086913303"],"corresponding_institution_ids":["https://openalex.org/I181679659"],"apc_list":null,"apc_paid":null,"fwci":1.7272,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.81709145,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"37","issue":"1","first_page":"381","last_page":"408"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9811000227928162,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.965399980545044,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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":0.8422524929046631},{"id":"https://openalex.org/keywords/symmetric-tensor","display_name":"Symmetric tensor","score":0.7056606411933899},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.703723669052124},{"id":"https://openalex.org/keywords/complex-conjugate","display_name":"Complex conjugate","score":0.6338744759559631},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.6285770535469055},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.5949872732162476},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5657500624656677},{"id":"https://openalex.org/keywords/power-sum-symmetric-polynomial","display_name":"Power sum symmetric polynomial","score":0.4694758355617523},{"id":"https://openalex.org/keywords/elementary-symmetric-polynomial","display_name":"Elementary symmetric polynomial","score":0.45356982946395874},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4490719735622406},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.4255492687225342},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.39211541414260864},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30254262685775757},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.22516992688179016},{"id":"https://openalex.org/keywords/macdonald-polynomials","display_name":"Macdonald polynomials","score":0.18773674964904785},{"id":"https://openalex.org/keywords/difference-polynomials","display_name":"Difference polynomials","score":0.14309996366500854},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.11009064316749573}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8422524929046631},{"id":"https://openalex.org/C20178491","wikidata":"https://www.wikidata.org/wiki/Q2204117","display_name":"Symmetric tensor","level":3,"score":0.7056606411933899},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.703723669052124},{"id":"https://openalex.org/C45542137","wikidata":"https://www.wikidata.org/wiki/Q381040","display_name":"Complex conjugate","level":2,"score":0.6338744759559631},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.6285770535469055},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.5949872732162476},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5657500624656677},{"id":"https://openalex.org/C129010115","wikidata":"https://www.wikidata.org/wiki/Q1298683","display_name":"Power sum symmetric polynomial","level":5,"score":0.4694758355617523},{"id":"https://openalex.org/C64338288","wikidata":"https://www.wikidata.org/wiki/Q2235316","display_name":"Elementary symmetric polynomial","level":4,"score":0.45356982946395874},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4490719735622406},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.4255492687225342},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39211541414260864},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30254262685775757},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.22516992688179016},{"id":"https://openalex.org/C171686973","wikidata":"https://www.wikidata.org/wiki/Q17098676","display_name":"Macdonald polynomials","level":4,"score":0.18773674964904785},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.14309996366500854},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.11009064316749573},{"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":3,"locations":[{"id":"doi:10.1137/141002256","is_oa":false,"landing_page_url":"https://doi.org/10.1137/141002256","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:CiteSeerX.psu:10.1.1.722.3390","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.722.3390","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.menet.umn.edu/%7Ezhangs/Reports/2015_JLZ.pdf","raw_type":"text"},{"id":"pmh:oai:researchportal.port.ac.uk:publications/96f0dbd3-1fac-4a51-9bf4-6063cf173ae9","is_oa":false,"landing_page_url":"https://researchportal.port.ac.uk/portal/en/publications/characterizing-realvalued-multivariate-complex-polynomials-and-their-symmetric-tensor-representations(96f0dbd3-1fac-4a51-9bf4-6063cf173ae9).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306401774","display_name":"Portsmouth Research Portal (University of Portsmouth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63072094","host_organization_name":"University of Portsmouth","host_organization_lineage":["https://openalex.org/I63072094"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2098721005","display_name":null,"funder_award_id":"CMMI-1462408","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8561488226","display_name":null,"funder_award_id":"11401364","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W35775221","https://openalex.org/W183398201","https://openalex.org/W802720919","https://openalex.org/W1491109205","https://openalex.org/W1583131051","https://openalex.org/W1852767571","https://openalex.org/W1970563156","https://openalex.org/W1973912509","https://openalex.org/W1979035610","https://openalex.org/W1985561227","https://openalex.org/W1986370957","https://openalex.org/W1989811026","https://openalex.org/W1993529825","https://openalex.org/W1996215314","https://openalex.org/W1996595848","https://openalex.org/W2007104311","https://openalex.org/W2007715285","https://openalex.org/W2010946668","https://openalex.org/W2012563130","https://openalex.org/W2013850411","https://openalex.org/W2013912476","https://openalex.org/W2024165284","https://openalex.org/W2034356527","https://openalex.org/W2039748980","https://openalex.org/W2065053468","https://openalex.org/W2069287942","https://openalex.org/W2070028074","https://openalex.org/W2076426934","https://openalex.org/W2084586233","https://openalex.org/W2088221456","https://openalex.org/W2090208105","https://openalex.org/W2090799283","https://openalex.org/W2095695857","https://openalex.org/W2099415732","https://openalex.org/W2113722075","https://openalex.org/W2126381689","https://openalex.org/W2143640815","https://openalex.org/W2150544307","https://openalex.org/W2163240983","https://openalex.org/W2163718799","https://openalex.org/W2165781304","https://openalex.org/W2526092852","https://openalex.org/W2589634431","https://openalex.org/W3102823452","https://openalex.org/W3140025309","https://openalex.org/W4233252806","https://openalex.org/W4236826464","https://openalex.org/W4289784446"],"related_works":["https://openalex.org/W2099781564","https://openalex.org/W2208476665","https://openalex.org/W2036077645","https://openalex.org/W2093789095","https://openalex.org/W4245102737","https://openalex.org/W2106114934","https://openalex.org/W2989730962","https://openalex.org/W4386113979","https://openalex.org/W2114613785","https://openalex.org/W1642716668"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,78,129],"study":[4,79],"multivariate":[5],"polynomial":[6],"functions":[7],"in":[8],"complex":[9,26,49,66,124,141],"variables":[10],"and":[11,40,55],"their":[12,57],"corresponding":[13,58],"symmetric":[14,37,84,98],"tensor":[15,59,99],"representations.":[16,60],"The":[17],"focus":[18],"is":[19,100,109],"to":[20,51,102],"find":[21],"conditions":[22,46],"under":[23],"which":[24],"such":[25,48],"polynomials":[27,50],"always":[28],"take":[29],"real":[30,53,97],"values.":[31],"We":[32,115],"introduce":[33],"the":[34,45,74,83,87,91,107,123,134,140],"notion":[35,136],"of":[36,63,82,95,133,137],"conjugate":[38,42],"forms":[39],"general":[41],"forms,":[43],"characterize":[44],"for":[47,65,122,139],"be":[52],"valued,":[54],"present":[56],"New":[61],"notions":[62],"eigenvalues/eigenvectors":[64,138],"tensors":[67],"are":[68],"introduced,":[69],"extending":[70],"similar":[71,119],"properties":[72],"from":[73],"Hermitian":[75],"matrices.":[76],"Moreover,":[77],"a":[80,96,118],"property":[81],"tensors,":[85],"namely,":[86],"largest":[88,104],"eigenvalue":[89],"(in":[90],"absolute":[92],"value":[93],"sense)":[94],"equal":[101],"its":[103],"singular":[105],"value;":[106],"result":[108,120],"also":[110],"known":[111],"as":[112,126],"Banach's":[113],"theorem.":[114],"show":[116],"that":[117],"holds":[121],"case":[125],"well.":[127],"Finally,":[128],"discuss":[130],"some":[131],"applications":[132],"new":[135],"tensors.":[142]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-17T18:11:37.981687","created_date":"2025-10-10T00:00:00"}