{"id":"https://openalex.org/W2026589607","doi":"https://doi.org/10.1137/s0895479896296908","title":"Cone Inclusion Numbers","display_name":"Cone Inclusion Numbers","publication_year":1998,"publication_date":"1998-07-01","ids":{"openalex":"https://openalex.org/W2026589607","doi":"https://doi.org/10.1137/s0895479896296908","mag":"2026589607"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479896296908","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479896296908","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/A5038208817","display_name":"Geir N\u00e6vdal","orcid":"https://orcid.org/0000-0003-2497-198X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Geir N\u00e6vdal","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5050951828","display_name":"Hugo J. Woerdeman","orcid":"https://orcid.org/0000-0002-8538-7173"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hugo J. Woerdeman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5057,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.6475251,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"3","first_page":"613","last_page":"639"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994999766349792,"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":0.9994999766349792,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/mathematics","display_name":"Mathematics","score":0.902071475982666},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7971296310424805},{"id":"https://openalex.org/keywords/infimum-and-supremum","display_name":"Infimum and supremum","score":0.6909705996513367},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5471594929695129},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4979679584503174},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.48926588892936707},{"id":"https://openalex.org/keywords/triangular-matrix","display_name":"Triangular matrix","score":0.48015183210372925},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.4586738049983978},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.41551342606544495},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.1193823516368866},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10798788070678711},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0929180383682251}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.902071475982666},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7971296310424805},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.6909705996513367},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5471594929695129},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4979679584503174},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.48926588892936707},{"id":"https://openalex.org/C104528550","wikidata":"https://www.wikidata.org/wiki/Q506265","display_name":"Triangular matrix","level":3,"score":0.48015183210372925},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.4586738049983978},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.41551342606544495},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.1193823516368866},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10798788070678711},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0929180383682251},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0},{"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:10.1137/s0895479896296908","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479896296908","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.7400000095367432}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W563112638","https://openalex.org/W996767716","https://openalex.org/W1485321578","https://openalex.org/W1510730180","https://openalex.org/W1575052616","https://openalex.org/W1965792141","https://openalex.org/W1983127118","https://openalex.org/W1983650664","https://openalex.org/W1985033420","https://openalex.org/W1987883983","https://openalex.org/W1992306716","https://openalex.org/W1998549987","https://openalex.org/W1998750273","https://openalex.org/W2006704773","https://openalex.org/W2013793368","https://openalex.org/W2018501141","https://openalex.org/W2022417522","https://openalex.org/W2033227498","https://openalex.org/W2034599918","https://openalex.org/W2034769312","https://openalex.org/W2051847003","https://openalex.org/W2059183447","https://openalex.org/W2062124264","https://openalex.org/W2064066631","https://openalex.org/W2065421822","https://openalex.org/W2066545547","https://openalex.org/W2070080181","https://openalex.org/W2075931151","https://openalex.org/W2088714191","https://openalex.org/W2089024379","https://openalex.org/W2091595279","https://openalex.org/W2144787788","https://openalex.org/W2145171684","https://openalex.org/W2367519446","https://openalex.org/W2610857016","https://openalex.org/W2912391444","https://openalex.org/W2983896310","https://openalex.org/W4214887864"],"related_works":["https://openalex.org/W2953175190","https://openalex.org/W4288318511","https://openalex.org/W2257286100","https://openalex.org/W2784344684","https://openalex.org/W2562705109","https://openalex.org/W3130072254","https://openalex.org/W123523165","https://openalex.org/W1800710304","https://openalex.org/W4294590026","https://openalex.org/W3022748053"],"abstract_inverted_index":{"The":[0],"introduction":[1],"of":[2,41,79],"cone":[3],"inclusion":[4],"numbers":[5],"allows":[6],"one":[7,14,106],"to":[8],"view":[9],"seemingly":[10],"different":[11],"problems":[12],"from":[13],"general":[15],"perspective.":[16],"Using":[17],"this":[18],"perspective":[19],"several":[20],"new":[21],"results":[22],"are":[23],"obtained,":[24],"such":[25],"as:":[26],"(a)":[27],"the":[28,39,74,90],"distance":[29],"constant":[30],"for":[31,58,72],"$\\TT_n":[32,36],"\\otimes":[33],"\\TT_n$,":[34],"where":[35],"$":[37],"denotes":[38],"algebra":[40],"n":[42,44,62,66,68],"x":[43,67],"strictly":[45],"upper":[46],"triangular":[47],"matrices,":[48],"is":[49,82,109],"bounded":[50],"above":[51],"by":[52],"[log2n":[53],"]":[54],"+":[55],"1$;":[56],"(b)":[57],"every":[59],"natural":[60],"number":[61],"there":[63],"exists":[64],"an":[65],"partial":[69],"correlation":[70],"matrix":[71],"which":[73],"largest":[75],"possible":[76,92],"minimal":[77],"eigenvalue":[78],"a":[80,104],"completion":[81],"$1":[83],"-":[84],"\\sqrt{\\lfloor":[85],"\\frac{n}{2}":[86],"\\rfloor}$;":[87],"and":[88],"(c)":[89],"lowest":[91],"entry-wise":[93],"supremum":[94],"norm":[95,105],"among":[96],"all":[97],"$n":[98],"\\times":[99],"n$":[100],"matrices":[101],"that":[102],"induce":[103],"Schur":[107],"map":[108],"$\\frac{1}{\\sqrt{n}}$.":[110]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
