{"id":"https://openalex.org/W2963217065","doi":"https://doi.org/10.1109/tit.2019.2913874","title":"Geometric Distance Between Positive Definite Matrices of Different Dimensions","display_name":"Geometric Distance Between Positive Definite Matrices of Different Dimensions","publication_year":2019,"publication_date":"2019-04-30","ids":{"openalex":"https://openalex.org/W2963217065","doi":"https://doi.org/10.1109/tit.2019.2913874","mag":"2963217065"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2019.2913874","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2019.2913874","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/A5050794507","display_name":"Lek\u2010Heng Lim","orcid":"https://orcid.org/0000-0002-9808-0138"},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]},{"id":"https://openalex.org/I4210131439","display_name":"Applied Mathematics (United States)","ror":"https://ror.org/03seew607","country_code":"US","type":"company","lineage":["https://openalex.org/I4210131439"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lek-Heng Lim","raw_affiliation_strings":["Computational and Applied Mathematics Initiative, The University of Chicago, Chicago, IL, USA"],"raw_orcid":"https://orcid.org/0000-0002-9808-0138","affiliations":[{"raw_affiliation_string":"Computational and Applied Mathematics Initiative, The University of Chicago, Chicago, IL, USA","institution_ids":["https://openalex.org/I40347166","https://openalex.org/I4210131439"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067642477","display_name":"Rodolphe Sepulchre","orcid":"https://orcid.org/0000-0002-7047-3124"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Rodolphe Sepulchre","raw_affiliation_strings":["Department of Engineering, University of Cambridge, Cambridge, U.K"],"raw_orcid":"https://orcid.org/0000-0002-7047-3124","affiliations":[{"raw_affiliation_string":"Department of Engineering, University of Cambridge, Cambridge, U.K","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100775242","display_name":"Ke Ye","orcid":"https://orcid.org/0000-0002-3193-7264"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ke Ye","raw_affiliation_strings":["KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9844,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.74853436,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"65","issue":"9","first_page":"5401","last_page":"5405"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9855999946594238,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9855999946594238,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.982200026512146,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9771999716758728,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.7603447437286377},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5474867224693298},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.43878403306007385},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.16716846823692322},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15715253353118896}],"concepts":[{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.7603447437286377},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5474867224693298},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43878403306007385},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.16716846823692322},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15715253353118896},{"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:10.1109/tit.2019.2913874","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2019.2913874","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":[{"id":"https://openalex.org/G2771606194","display_name":null,"funder_award_id":"D15AP00109","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G529999276","display_name":"A multi-resolution theory for systems and control across scales","funder_award_id":"670645","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G5686484291","display_name":null,"funder_award_id":"IIS 1546413","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6967058303","display_name":null,"funder_award_id":"11688101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8698799443","display_name":null,"funder_award_id":"11801548","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/F4320309626","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321133","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1514337951","https://openalex.org/W1969002377","https://openalex.org/W1983104971","https://openalex.org/W1983496390","https://openalex.org/W2005577322","https://openalex.org/W2059640215","https://openalex.org/W2068787860","https://openalex.org/W2118443009","https://openalex.org/W2154059477","https://openalex.org/W2963346868","https://openalex.org/W4211084734","https://openalex.org/W4245345046","https://openalex.org/W4249121476","https://openalex.org/W4250589301"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W2333431385","https://openalex.org/W3086542228","https://openalex.org/W2122837848","https://openalex.org/W2017331178","https://openalex.org/W2976797620","https://openalex.org/W2260035625","https://openalex.org/W2331735732","https://openalex.org/W4223579399","https://openalex.org/W2009650958"],"abstract_inverted_index":{"We":[0],"show":[1],"how":[2],"the":[3,15],"geodesic":[4],"distance":[5,41,89],"on":[6,64],"S":[7,51],"<sub":[8,52],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[9,12,53,56,67],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">++</sub>":[10,54],"<sup":[11,55,66],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sup>":[13,57,68],",":[14,69],"cone":[16],"of":[17,46,75,93,96],"n":[18,20,71,73],"\u00d7":[19,72],"real":[21],"symmetric":[22],"or":[23],"complex":[24],"Hermitian":[25],"positive":[26],"definite":[27],"matrices":[28,45],"regarded":[29],"as":[30],"a":[31,40,82,87,91],"Riemannian":[32],"manifold,":[33],"may":[34],"be":[35],"used":[36],"to":[37,85],"naturally":[38],"define":[39,86],"between":[42,90],"two":[43],"such":[44,94],"different":[47,97],"dimensions.":[48,98],"Given":[49],"that":[50],"also":[58],"parameterizes":[59],"n-dimensional":[60],"ellipsoids,":[61],"inner":[62],"products":[63],"\u211d":[65],"and":[70],"covariances":[74],"nondegenerate":[76],"probability":[77],"distributions,":[78],"this":[79],"gives":[80],"us":[81],"natural":[83],"way":[84],"geometric":[88],"pair":[92],"objects":[95]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}