{"id":"https://openalex.org/W2228640577","doi":"https://doi.org/10.48550/arxiv.1509.00748","title":"An elementary approach to the problem of column selection in a rectangular matrix","display_name":"An elementary approach to the problem of column selection in a rectangular matrix","publication_year":2015,"publication_date":"2015-09-02","ids":{"openalex":"https://openalex.org/W2228640577","doi":"https://doi.org/10.48550/arxiv.1509.00748","mag":"2228640577"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1509.00748","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1509.00748","pdf_url":"https://arxiv.org/pdf/1509.00748","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1509.00748","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059835438","display_name":"St\u00e9phane Chr\u00e9tien","orcid":"https://orcid.org/0000-0002-4544-1315","observed_orcids":["https://orcid.org/0000-0002-4544-1315"]},"institutions":[{"id":"https://openalex.org/I4387152972","display_name":"Laboratoire de Math\u00e9matiques de Besan\u00e7on","ror":"https://ror.org/04nrhwg12","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4387152972","https://openalex.org/I4405256580"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Chretien, Stephane","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques de Besan\u00e7on (UMR 6623)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques de Besan\u00e7on (UMR 6623)","institution_ids":["https://openalex.org/I4387152972"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111846760","display_name":"S\u00e9bastien Darses","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210138206","display_name":"Institut de Math\u00e9matiques de Marseille","ror":"https://ror.org/042h2y225","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210138206","https://openalex.org/I4210141950","https://openalex.org/I4210142724"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Darses, Sebastien","raw_affiliation_strings":["Institut de Math\u00e9matiques de Marseille"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Marseille","institution_ids":["https://openalex.org/I4210138206"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.5746999979019165,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11545","display_name":"Advanced Banach Space Theory","score":0.5746999979019165,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.133200004696846,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.05999999865889549,"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/column-selection","display_name":"column selection","score":0.9829999804496765},{"id":"https://openalex.org/keywords/rectangular-matrices","display_name":"rectangular matrices","score":0.968999981880188},{"id":"https://openalex.org/keywords/singular-values","display_name":"singular values","score":0.8669999837875366},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"upper and lower bounds","score":0.6779999732971191}],"concepts":[{"id":"https://openalex.org/C2780551164","wikidata":"https://www.wikidata.org/wiki/Q2306599","display_name":"Column (typography)","level":3,"score":0.7088900208473206},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.6895028352737427},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5870678424835205},{"id":"https://openalex.org/C96442811","wikidata":"https://www.wikidata.org/wiki/Q609566","display_name":"Elementary matrix","level":3,"score":0.541364312171936},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4263918101787567},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3787321448326111},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21938860416412354},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.1757822334766388},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.10289579629898071},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08969339728355408},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08588176965713501},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.0},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:1509.00748","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1509.00748","pdf_url":"https://arxiv.org/pdf/1509.00748","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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-01270800v1","doi":null,"is_oa":false,"landing_page_url":"https://hal.science/hal-01270800","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2016","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.1509.00748","doi":"https://doi.org/10.48550/arxiv.1509.00748","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1509.00748","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1509.00748","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1509.00748","pdf_url":"https://arxiv.org/pdf/1509.00748","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2228640577.pdf","grobid_xml":"https://content.openalex.org/works/W2228640577.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1997889147","https://openalex.org/W2034070643","https://openalex.org/W2039508082","https://openalex.org/W2071824193","https://openalex.org/W3105179449"],"related_works":["https://openalex.org/W2937950107","https://openalex.org/W2263873406","https://openalex.org/W4311632802","https://openalex.org/W7100699696","https://openalex.org/W2796016873","https://openalex.org/W2114983089","https://openalex.org/W7095482931","https://openalex.org/W6966814921","https://openalex.org/W2161921901","https://openalex.org/W7151871583"],"abstract_inverted_index":{"The":[0,47],"problem":[1,50],"of":[2,45,85,92,101,110],"extracting":[3,59],"a":[4,60,65],"well":[5,61],"conditioned":[6,62],"submatrix":[7],"from":[8],"any":[9],"rectangular":[10],"matrix":[11,66,88],"(with":[12],"normalized":[13],"columns)":[14],"has":[15],"been":[16,38],"studied":[17],"for":[18,28,81],"some":[19],"time":[20],"in":[21,53,72,98],"functional":[22],"and":[23,78,112,119,124],"harmonic":[24],"analysis;":[25],"see":[26,41],"\\cite{BourgainTzafriri:IJM87,Tropp:StudiaMath08,Vershynin:IJM01}":[27],"methods":[29],"using":[30],"random":[31],"column":[32,48],"selection.":[33],"More":[34],"constructive":[35,118],"approaches":[36],"have":[37],"proposed":[39],"recently;":[40],"the":[42,86,90,99,106,120],"recent":[43],"contributions":[44],"\\cite{SpielmanSrivastava:IJM12,Youssef:IMRN14}.":[46],"selection":[49],"we":[51],"consider":[52],"this":[54],"paper":[55],"is":[56,116,122],"concerned":[57],"with":[58],"submatrix,":[63],"i.e.":[64],"whose":[67],"singular":[68,83],"values":[69],"all":[70],"lie":[71],"$[1-\u03b5,1+\u03b5]$.":[73],"We":[74],"provide":[75],"individual":[76],"lower":[77],"upper":[79],"bounds":[80],"each":[82],"value":[84],"extracted":[87],"at":[89],"price":[91],"conceding":[93],"only":[94],"one":[95],"log":[96],"factor":[97],"number":[100],"columns,":[102],"when":[103],"compared":[104],"to":[105],"Restricted":[107],"Invertibility":[108],"Theorem":[109],"Bourgain":[111],"Tzafriri.":[113],"Our":[114],"method":[115],"fully":[117],"proof":[121],"short":[123],"elementary.":[125]},"counts_by_year":[{"year":2018,"cited_by_count":2}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2025-10-10T00:00:00"}
