{"id":"https://openalex.org/W2081099116","doi":"https://doi.org/10.1137/s0895479803437827","title":"Compressions of Totally Positive Matrices","display_name":"Compressions of Totally Positive Matrices","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2081099116","doi":"https://doi.org/10.1137/s0895479803437827","mag":"2081099116"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479803437827","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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5000272528","display_name":"Shaun Fallat","orcid":"https://orcid.org/0000-0002-7185-7357"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shaun M. Fallat","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058114904","display_name":"Allen Herman","orcid":"https://orcid.org/0000-0001-9841-636X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Allen Herman","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110628608","display_name":"Michael Gekhtman","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael I. Gekhtman","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5111066366","display_name":"Charles R. Johnson","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Charles R. Johnson","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.819,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":12,"citation_normalized_percentile":{"value":0.786934,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":83,"max":84},"biblio":{"volume":"28","issue":"1","first_page":"68","last_page":"80"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9995,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9995,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9971,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9918,"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/matrix","display_name":"Matrix (chemical analysis)","score":0.70510566},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.5973526}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8108573},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.70510566},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6335876},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6190908},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.5973526},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.45624888},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.42431393},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.091905266},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.05318609},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.052513927},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479803437827","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":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":16,"referenced_works":["https://openalex.org/W1912422805","https://openalex.org/W1987225390","https://openalex.org/W2002168116","https://openalex.org/W2008334721","https://openalex.org/W2023446880","https://openalex.org/W2029964383","https://openalex.org/W2035133303","https://openalex.org/W2047405850","https://openalex.org/W2054663063","https://openalex.org/W2067894710","https://openalex.org/W2094302535","https://openalex.org/W2323480894","https://openalex.org/W2334457461","https://openalex.org/W4246632628","https://openalex.org/W4248658188","https://openalex.org/W614920821"],"related_works":["https://openalex.org/W4300656036","https://openalex.org/W4251679243","https://openalex.org/W3033252460","https://openalex.org/W2964184729","https://openalex.org/W2611130496","https://openalex.org/W2360264057","https://openalex.org/W2219025096","https://openalex.org/W1995893205","https://openalex.org/W1995891825","https://openalex.org/W1984430553"],"abstract_inverted_index":{"A":[0,17,60],"matrix":[1,16,42,58,89,94],"is":[2,18,30,47,70],"called":[3],"totally":[4,14,49,92,98],"positive":[5,15,50,93],"if":[6],"all":[7],"its":[8],"minors":[9],"are":[10],"positive.":[11,99],"If":[12],"a":[13,91],"partitioned":[19],"as":[20],"$A":[21],"=":[22],"(A_{ij})$":[23],"$i,j=1,2,\\ldots,k$,":[24],"in":[25],"which":[26],"each":[27],"block":[28],"$A_{ij}$":[29],"n":[31],"x":[32,39,86],"n,":[33],"we":[34,79],"show":[35],"that":[36,52,65,83],"the":[37,53,56,84],"k":[38,40,85,87],"compressed":[41,57,88],"given":[43],"by":[44,81],"$(\\det":[45],"A_{ij})$":[46],"also":[48,71],"and":[51],"determinant":[54],"of":[55,90],"exceeds":[59],"when":[61,73],"k=2,3.":[62,74],"An":[63],"extension":[64],"allows":[66],"for":[67],"overlapping":[68],"blocks":[69],"presented":[72],"For":[75],"$k":[76],"\\geq":[77],"4$":[78],"verify,":[80],"example,":[82],"need":[95],"not":[96],"be":[97]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2081099116","counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2024-12-12T02:16:57.926371","created_date":"2016-06-24"}