{"id":"https://openalex.org/W2956568790","doi":"https://doi.org/10.1137/19m1286578","title":"Kippenhahn's Theorem for Joint Numerical Ranges and Quantum States","display_name":"Kippenhahn's Theorem for Joint Numerical Ranges and Quantum States","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W2956568790","doi":"https://doi.org/10.1137/19m1286578","mag":"2956568790"},"language":"en","primary_location":{"id":"doi:10.1137/19m1286578","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1286578","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/1907.04768","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Daniel Plaumann","orcid":"https://orcid.org/0000-0002-3376-6841"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Daniel Plaumann","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-3376-6841","affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Rainer Sinn","orcid":"https://orcid.org/0000-0001-9456-6889"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rainer Sinn","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-9456-6889","affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Stephan Weis","orcid":"https://orcid.org/0000-0003-1316-9115"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stephan Weis","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-1316-9115","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.757,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.73992202,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"5","issue":"1","first_page":"86","last_page":"113"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.5360999703407288,"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":0.5360999703407288,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.07980000227689743,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied 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/T10020","display_name":"Quantum Information and Cryptography","score":0.0689999982714653,"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/numerical-range","display_name":"Numerical range","score":0.8064000010490417},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.7617999911308289},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.6783999800682068},{"id":"https://openalex.org/keywords/convex-cone","display_name":"Convex cone","score":0.5950000286102295},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.47999998927116394},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4641999900341034},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4352000057697296},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4250999987125397},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.40380001068115234},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.38839998841285706}],"concepts":[{"id":"https://openalex.org/C193060811","wikidata":"https://www.wikidata.org/wiki/Q1579053","display_name":"Numerical range","level":2,"score":0.8064000010490417},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.7617999911308289},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7263000011444092},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.6783999800682068},{"id":"https://openalex.org/C28340159","wikidata":"https://www.wikidata.org/wiki/Q2256541","display_name":"Convex cone","level":5,"score":0.5950000286102295},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4869000017642975},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.47999998927116394},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4641999900341034},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4352000057697296},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4250999987125397},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.40380001068115234},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.38839998841285706},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.38260000944137573},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.38019999861717224},{"id":"https://openalex.org/C18555067","wikidata":"https://www.wikidata.org/wiki/Q8375051","display_name":"Joint (building)","level":2,"score":0.3774999976158142},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.3450999855995178},{"id":"https://openalex.org/C37423430","wikidata":"https://www.wikidata.org/wiki/Q6750281","display_name":"Hull","level":2,"score":0.3402000069618225},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3391999900341034},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.3382999897003174},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.3370000123977661},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.32850000262260437},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.32339999079704285},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.3158000111579895},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3068000078201294},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.3012999892234802},{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.298799991607666},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.2987000048160553},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.29589998722076416},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.28760001063346863},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28299999237060547},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2799000144004822},{"id":"https://openalex.org/C2776230367","wikidata":"https://www.wikidata.org/wiki/Q7314222","display_name":"Representation theorem","level":2,"score":0.26170000433921814},{"id":"https://openalex.org/C30072841","wikidata":"https://www.wikidata.org/wiki/Q1767080","display_name":"Diagonalizable matrix","level":4,"score":0.25850000977516174}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/19m1286578","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1286578","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:1907.04768","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1907.04768","pdf_url":"https://arxiv.org/pdf/1907.04768","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1907.04768","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1907.04768","pdf_url":"https://arxiv.org/pdf/1907.04768","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W1552713971","https://openalex.org/W1820769125","https://openalex.org/W1978924226","https://openalex.org/W1993304213","https://openalex.org/W1996970467","https://openalex.org/W1998626963","https://openalex.org/W1999791015","https://openalex.org/W2000844563","https://openalex.org/W2002497815","https://openalex.org/W2015936613","https://openalex.org/W2016143735","https://openalex.org/W2020081642","https://openalex.org/W2021887341","https://openalex.org/W2023886978","https://openalex.org/W2025202934","https://openalex.org/W2028398220","https://openalex.org/W2031249960","https://openalex.org/W2055465902","https://openalex.org/W2065056910","https://openalex.org/W2071293323","https://openalex.org/W2071819488","https://openalex.org/W2072329172","https://openalex.org/W2075312216","https://openalex.org/W2084226713","https://openalex.org/W2088097425","https://openalex.org/W2089121071","https://openalex.org/W2149308998","https://openalex.org/W2150731547","https://openalex.org/W2152309892","https://openalex.org/W2156719288","https://openalex.org/W2309751936","https://openalex.org/W2463493049","https://openalex.org/W2468750585","https://openalex.org/W2592990935","https://openalex.org/W2774546339","https://openalex.org/W2920941962","https://openalex.org/W2962712276","https://openalex.org/W2962795926","https://openalex.org/W2962948712","https://openalex.org/W2962984804","https://openalex.org/W2963673026","https://openalex.org/W3047604236","https://openalex.org/W3092347397"],"related_works":[],"abstract_inverted_index":{"Kippenhahn's":[0],"theorem":[1],"asserts":[2],"that":[3,22,57],"the":[4,11,23,34,47,58],"numerical":[5,25],"range":[6,26],"of":[7,14,27,37,60,62],"a":[8,15,38,52,74],"matrix":[9],"is":[10,32,66],"convex":[12,35,49],"hull":[13,36],"certain":[16],"algebraic":[17],"curve.":[18],"Here,":[19],"we":[20],"show":[21],"joint":[24],"finitely":[28],"many":[29],"Hermitian":[30],"matrices":[31],"similarly":[33],"semialgebraic":[39],"set.":[40],"We":[41],"discuss":[42],"an":[43],"analogous":[44],"statement":[45],"regarding":[46],"dual":[48,64],"cone":[50,54],"to":[51,78],"hyperbolicity":[53],"and":[55],"prove":[56],"class":[59],"bases":[61],"these":[63],"cones":[65],"closed":[67],"under":[68],"linear":[69],"operations.":[70],"The":[71],"result":[72],"offers":[73],"new":[75],"geometric":[76],"method":[77],"analyze":[79],"quantum":[80],"states.":[81]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2019-07-23T00:00:00"}
