{"id":"https://openalex.org/W2071902861","doi":"https://doi.org/10.1137/s0895479891201201","title":"Norms of Hadamard Multipliers","display_name":"Norms of Hadamard Multipliers","publication_year":1994,"publication_date":"1994-01-01","ids":{"openalex":"https://openalex.org/W2071902861","doi":"https://doi.org/10.1137/s0895479891201201","mag":"2071902861"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479891201201","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479891201201","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/A5010703644","display_name":"Carl C. Cowen","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Carl C. Cowen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016400429","display_name":"Michael A. Dritschel","orcid":"https://orcid.org/0000-0002-9465-0682"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael A. Dritschel","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108339061","display_name":"Richard Penney","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Richard C. Penney","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5010703644"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.9058,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.90635048,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"15","issue":"1","first_page":"313","last_page":"320"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.9998000264167786,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.9998000264167786,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T10884","display_name":"Holomorphic and Operator Theory","score":0.9993000030517578,"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/mathematics","display_name":"Mathematics","score":0.8144439458847046},{"id":"https://openalex.org/keywords/complex-hadamard-matrix","display_name":"Complex Hadamard matrix","score":0.8124023675918579},{"id":"https://openalex.org/keywords/hadamard-product","display_name":"Hadamard product","score":0.6900989413261414},{"id":"https://openalex.org/keywords/hadamard-matrix","display_name":"Hadamard matrix","score":0.6877449154853821},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.6634347438812256},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.6505561470985413},{"id":"https://openalex.org/keywords/hadamards-inequality","display_name":"Hadamard's inequality","score":0.6377270817756653},{"id":"https://openalex.org/keywords/hadamards-maximal-determinant-problem","display_name":"Hadamard's maximal determinant problem","score":0.6342002153396606},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.5673301815986633},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.5134797692298889},{"id":"https://openalex.org/keywords/hadamard-three-lines-theorem","display_name":"Hadamard three-lines theorem","score":0.4944932460784912},{"id":"https://openalex.org/keywords/hadamard-three-circle-theorem","display_name":"Hadamard three-circle theorem","score":0.458467572927475},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4542577266693115},{"id":"https://openalex.org/keywords/operator-norm","display_name":"Operator norm","score":0.4286420941352844},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.4267267882823944},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4143456518650055},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4002211093902588},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.383749783039093},{"id":"https://openalex.org/keywords/operator-theory","display_name":"Operator theory","score":0.25456398725509644},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.2543651759624481},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20685744285583496},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.09596771001815796}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8144439458847046},{"id":"https://openalex.org/C6497535","wikidata":"https://www.wikidata.org/wiki/Q5156556","display_name":"Complex Hadamard matrix","level":4,"score":0.8124023675918579},{"id":"https://openalex.org/C90230998","wikidata":"https://www.wikidata.org/wiki/Q3406746","display_name":"Hadamard product","level":3,"score":0.6900989413261414},{"id":"https://openalex.org/C30463267","wikidata":"https://www.wikidata.org/wiki/Q1422682","display_name":"Hadamard matrix","level":3,"score":0.6877449154853821},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.6634347438812256},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.6505561470985413},{"id":"https://openalex.org/C31021346","wikidata":"https://www.wikidata.org/wiki/Q1365087","display_name":"Hadamard's inequality","level":4,"score":0.6377270817756653},{"id":"https://openalex.org/C121334634","wikidata":"https://www.wikidata.org/wiki/Q5637579","display_name":"Hadamard's maximal determinant problem","level":5,"score":0.6342002153396606},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.5673301815986633},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.5134797692298889},{"id":"https://openalex.org/C68720959","wikidata":"https://www.wikidata.org/wiki/Q3527250","display_name":"Hadamard three-lines theorem","level":4,"score":0.4944932460784912},{"id":"https://openalex.org/C35222485","wikidata":"https://www.wikidata.org/wiki/Q729359","display_name":"Hadamard three-circle theorem","level":5,"score":0.458467572927475},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4542577266693115},{"id":"https://openalex.org/C68386474","wikidata":"https://www.wikidata.org/wiki/Q980557","display_name":"Operator norm","level":3,"score":0.4286420941352844},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4267267882823944},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4143456518650055},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4002211093902588},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.383749783039093},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.25456398725509644},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.2543651759624481},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20685744285583496},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.09596771001815796},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0895479891201201","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479891201201","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.491.4963","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.491.4963","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.iupui.edu/~ccowen/Downloads/32HadNorm.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.47999998927116394}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W1569948236","https://openalex.org/W1586975367","https://openalex.org/W1678167890","https://openalex.org/W2018501141","https://openalex.org/W2060193099","https://openalex.org/W2064066631","https://openalex.org/W4255788608"],"related_works":["https://openalex.org/W2138472192","https://openalex.org/W4226106482","https://openalex.org/W1976224891","https://openalex.org/W2072949187","https://openalex.org/W2061168688","https://openalex.org/W2950772023","https://openalex.org/W1971692815","https://openalex.org/W3154819821","https://openalex.org/W2032706668","https://openalex.org/W2026768906"],"abstract_inverted_index":{"For":[0],"B":[1],"a":[2,38,60,88,97,107],"fixed":[3],"matrix,":[4],"the":[5,8,12,15,27,35,47,52,104],"authors":[6],"consider":[7],"problem":[9,53,62],"of":[10,14,32,37,49,87,99,106],"finding":[11],"norm":[13,36,78],"map":[16],"$X":[17],"\\mapsto":[18],"X":[19],"\\bullet":[20,24],"B$,":[21],"where":[22],"$":[23,25],"is":[26,40,54,83],"Hadamard":[28,76],"or":[29],"entrywise":[30],"product":[31],"matrices":[33,58],"and":[34],"matrix":[39,82],"its":[41],"spectral":[42],"norm.":[43],"Using":[44],"techniques":[45],"from":[46,71],"theory":[48],"Kren":[50],"spaces,":[51],"rewritten":[55],"for":[56,65,79],"Hermitian":[57,89],"as":[59],"minimization":[61],"whose":[63],"solution,":[64],"small":[66],"matrices,":[67],"can":[68],"be":[69],"obtained":[70],"standard":[72],"optimization":[73],"software.":[74],"The":[75,91],"multiplier":[77],"an":[80,110],"arbitrary":[81],"given":[84],"in":[85,109],"terms":[86],"extension.":[90],"results":[92],"are":[93],"applied":[94],"to":[95],"refute":[96],"conjecture":[98],"R.":[100],"V.":[101],"McEachin":[102],"concerning":[103],"value":[105],"constant":[108],"operator":[111],"inequality.":[112]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
