{"id":"https://openalex.org/W2110649199","doi":"https://doi.org/10.1007/s11075-006-9046-2","title":"The many proofs of an identity on the norm of oblique projections","display_name":"The many proofs of an identity on the norm of oblique projections","publication_year":2006,"publication_date":"2006-10-27","ids":{"openalex":"https://openalex.org/W2110649199","doi":"https://doi.org/10.1007/s11075-006-9046-2","mag":"2110649199"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-006-9046-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-006-9046-2","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","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/A5047875137","display_name":"Daniel B. Szyld","orcid":"https://orcid.org/0000-0001-8010-0391"},"institutions":[{"id":"https://openalex.org/I84392919","display_name":"Temple University","ror":"https://ror.org/00kx1jb78","country_code":"US","type":"education","lineage":["https://openalex.org/I84392919"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Daniel B. Szyld","raw_affiliation_strings":["Department of Mathematics, Temple University, Philadelphia, PA, 19122, USA","[Temple University]"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Temple University, Philadelphia, PA, 19122, USA","institution_ids":["https://openalex.org/I84392919"]},{"raw_affiliation_string":"[Temple University]","institution_ids":["https://openalex.org/I84392919"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5047875137"],"corresponding_institution_ids":["https://openalex.org/I84392919"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":3.7072,"has_fulltext":false,"cited_by_count":134,"citation_normalized_percentile":{"value":0.93234579,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"42","issue":"3-4","first_page":"309","last_page":"323"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9980999827384949,"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":0.9972000122070312,"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":0.849982738494873},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.8349656462669373},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.7064452171325684},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.666858971118927},{"id":"https://openalex.org/keywords/oblique-case","display_name":"Oblique case","score":0.6075074076652527},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.552969753742218},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.5440070629119873},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.46716535091400146},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4608224630355835},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3388165831565857},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15507721900939941},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14946675300598145},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.10745000839233398},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.06781437993049622}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.849982738494873},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.8349656462669373},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.7064452171325684},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.666858971118927},{"id":"https://openalex.org/C160697094","wikidata":"https://www.wikidata.org/wiki/Q1233197","display_name":"Oblique case","level":2,"score":0.6075074076652527},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.552969753742218},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.5440070629119873},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.46716535091400146},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4608224630355835},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3388165831565857},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15507721900939941},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14946675300598145},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.10745000839233398},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.06781437993049622},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11075-006-9046-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-006-9046-2","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.331.1882","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.331.1882","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://math.temple.edu/~szyld/reports/proj_report.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4300000071525574,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W83404773","https://openalex.org/W131753375","https://openalex.org/W601358444","https://openalex.org/W658559791","https://openalex.org/W832956562","https://openalex.org/W1485916122","https://openalex.org/W1487444668","https://openalex.org/W1500523287","https://openalex.org/W1541694600","https://openalex.org/W1557106406","https://openalex.org/W1560592371","https://openalex.org/W1575147392","https://openalex.org/W1973683994","https://openalex.org/W1981745143","https://openalex.org/W1984263725","https://openalex.org/W1993483669","https://openalex.org/W2021411519","https://openalex.org/W2029015714","https://openalex.org/W2035842194","https://openalex.org/W2042739535","https://openalex.org/W2048488460","https://openalex.org/W2060850998","https://openalex.org/W2063683773","https://openalex.org/W2064878022","https://openalex.org/W2069739859","https://openalex.org/W2087142053","https://openalex.org/W2087399108","https://openalex.org/W2089196355","https://openalex.org/W2094553393","https://openalex.org/W2106619956","https://openalex.org/W2125422126","https://openalex.org/W2132659887","https://openalex.org/W2139940635","https://openalex.org/W2154427710","https://openalex.org/W2161347185","https://openalex.org/W2167829188","https://openalex.org/W2183231791","https://openalex.org/W2331224188","https://openalex.org/W2419464796","https://openalex.org/W2583829122","https://openalex.org/W2798909945","https://openalex.org/W3030910590","https://openalex.org/W3150353689","https://openalex.org/W4239727685","https://openalex.org/W4300657400","https://openalex.org/W4301621763"],"related_works":["https://openalex.org/W2808944898","https://openalex.org/W2385104873","https://openalex.org/W2150654092","https://openalex.org/W3196207352","https://openalex.org/W2951724202","https://openalex.org/W3084261076","https://openalex.org/W1996614773","https://openalex.org/W4387820098","https://openalex.org/W2576399385","https://openalex.org/W2963408011"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}