{"id":"https://openalex.org/W3140295493","doi":"https://doi.org/10.1137/21m1412980","title":"On Tensors That Are Determined by Their Singular Tuples","display_name":"On Tensors That Are Determined by Their Singular Tuples","publication_year":2022,"publication_date":"2022-06-01","ids":{"openalex":"https://openalex.org/W3140295493","doi":"https://doi.org/10.1137/21m1412980","mag":"3140295493"},"language":"en","primary_location":{"id":"doi:10.1137/21m1412980","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1412980","pdf_url":null,"source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"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 Applied Algebra and Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2104.03686","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050530390","display_name":"Ettore Teixeira Turatti","orcid":"https://orcid.org/0000-0003-4953-3994"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ettore Turatti","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-4953-3994","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050530390"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8201,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.68345324,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"6","issue":"2","first_page":"319","last_page":"338"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9916999936103821,"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":0.9916999936103821,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.0008999999845400453,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.000699999975040555,"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/tuple","display_name":"Tuple","score":0.8599299192428589},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7967609167098999},{"id":"https://openalex.org/keywords/hypersurface","display_name":"Hypersurface","score":0.7412377595901489},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.6168459057807922},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5741217136383057},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.5598421096801758},{"id":"https://openalex.org/keywords/locus","display_name":"Locus (genetics)","score":0.4310847818851471},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3435191512107849},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.22566735744476318}],"concepts":[{"id":"https://openalex.org/C118930307","wikidata":"https://www.wikidata.org/wiki/Q600590","display_name":"Tuple","level":2,"score":0.8599299192428589},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7967609167098999},{"id":"https://openalex.org/C114410712","wikidata":"https://www.wikidata.org/wiki/Q973321","display_name":"Hypersurface","level":2,"score":0.7412377595901489},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.6168459057807922},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5741217136383057},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5598421096801758},{"id":"https://openalex.org/C84597430","wikidata":"https://www.wikidata.org/wiki/Q106227","display_name":"Locus (genetics)","level":3,"score":0.4310847818851471},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3435191512107849},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.22566735744476318},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/21m1412980","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1412980","pdf_url":null,"source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"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 Applied Algebra and Geometry","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2104.03686","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2104.03686","pdf_url":"https://arxiv.org/pdf/2104.03686","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-03193911v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03193911","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Applied Algebra and Geometry, 2022, 6 (2), pp.319-338. ⟨10.1137/21M1412980⟩","raw_type":"Journal articles"},{"id":"pmh:oai:flore.unifi.it:2158/1291226","is_oa":false,"landing_page_url":"https://hdl.handle.net/2158/1291226","pdf_url":null,"source":{"id":"https://openalex.org/S4306402033","display_name":"Florence Research (University of Florence)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45084792","host_organization_name":"University of Florence","host_organization_lineage":["https://openalex.org/I45084792"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2104.03686","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2104.03686","pdf_url":"https://arxiv.org/pdf/2104.03686","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"score":0.6399999856948853,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G4535932799","display_name":null,"funder_award_id":"813211","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"}],"funders":[{"id":"https://openalex.org/F4320332999","display_name":"Horizon 2020 Framework Programme","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W804266481","https://openalex.org/W1951162345","https://openalex.org/W1970563156","https://openalex.org/W1977415556","https://openalex.org/W1993529825","https://openalex.org/W2053728908","https://openalex.org/W2123142168","https://openalex.org/W2124706092","https://openalex.org/W2125880378","https://openalex.org/W2421281141","https://openalex.org/W2949558083","https://openalex.org/W2963542075","https://openalex.org/W2963872471","https://openalex.org/W2963962955","https://openalex.org/W3080772264","https://openalex.org/W3166881127","https://openalex.org/W3172792678","https://openalex.org/W3207612017","https://openalex.org/W4212877249","https://openalex.org/W4245490374"],"related_works":["https://openalex.org/W834447687","https://openalex.org/W4239786835","https://openalex.org/W2952832090","https://openalex.org/W2040382607","https://openalex.org/W2121611394","https://openalex.org/W1582111390","https://openalex.org/W2154734935","https://openalex.org/W2951523575","https://openalex.org/W2949618778","https://openalex.org/W2950325999"],"abstract_inverted_index":{"In":[0],"this":[1,87],"paper":[2],"we":[3,19],"study":[4],"the":[5,26,38,48,55,58,62,70,93,98,102],"locus":[6],"of":[7,10,28,31],"singular":[8,29,44],"tuples":[9,30],"a":[11,66,105],"complex-valued":[12],"multisymmetric":[13],"tensor.":[14],"The":[15],"main":[16],"problem":[17],"that":[18,40,47,57],"focus":[20],"on":[21],"is":[22,53,65,89,104],"as":[23],"follows:":[24],"Given":[25],"set":[27],"some":[32],"general":[33],"tensor,":[34],"what":[35],"are":[36,100],"all":[37,97],"tensors":[39],"admit":[41],"those":[42],"same":[43],"tuples?":[45],"Assume":[46],"triangle":[49],"inequality":[50],"holds,":[51],"which":[52],"exactly":[54],"condition":[56],"dual":[59],"variety":[60,64],"to":[61],"Segre--Veronese":[63],"hypersurface,":[67],"or":[68],"equivalently,":[69],"hyperdeterminant":[71],"exists.":[72],"We":[73],"show":[74],"in":[75],"such":[76],"cases":[77],"that,":[78],"when":[79],"at":[80],"least":[81],"one":[82],"component":[83],"has":[84],"degree":[85],"odd,":[86],"tensor":[88],"projectively":[90],"unique.":[91],"On":[92],"other":[94],"hand,":[95],"if":[96],"degrees":[99],"even,":[101],"fiber":[103],"1-dimensional":[106],"space.":[107]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}