{"id":"https://openalex.org/W2002233832","doi":"https://doi.org/10.1137/s0895479895283409","title":"A Chain Rule for Matrix Functions and Applications","display_name":"A Chain Rule for Matrix Functions and Applications","publication_year":1996,"publication_date":"1996-07-01","ids":{"openalex":"https://openalex.org/W2002233832","doi":"https://doi.org/10.1137/s0895479895283409","mag":"2002233832"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479895283409","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479895283409","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/A5081622212","display_name":"Roy Mathias","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Roy Mathias","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5081622212"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":57,"citation_normalized_percentile":{"value":0.12976125,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"17","issue":"3","first_page":"610","last_page":"620"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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":1.0,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9940000176429749,"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"}},{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8285559415817261},{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.6749585270881653},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6379945278167725},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.6092158555984497},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.5775691270828247},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5564913749694824},{"id":"https://openalex.org/keywords/matrix-function","display_name":"Matrix function","score":0.5096104145050049},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48636892437934875},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4601583480834961},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4422530233860016},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3979952931404114},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.3772558569908142},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34988105297088623},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.08119544386863708}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8285559415817261},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.6749585270881653},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6379945278167725},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.6092158555984497},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5775691270828247},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5564913749694824},{"id":"https://openalex.org/C4263655","wikidata":"https://www.wikidata.org/wiki/Q2699958","display_name":"Matrix function","level":4,"score":0.5096104145050049},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48636892437934875},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4601583480834961},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4422530233860016},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3979952931404114},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.3772558569908142},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34988105297088623},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.08119544386863708},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"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/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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895479895283409","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479895283409","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1488435683","https://openalex.org/W1967351325","https://openalex.org/W1993865925","https://openalex.org/W1996268937","https://openalex.org/W2015001720","https://openalex.org/W2020054862","https://openalex.org/W2039968554","https://openalex.org/W2060530093","https://openalex.org/W2067136705","https://openalex.org/W2171978643","https://openalex.org/W2797638056","https://openalex.org/W4246939581","https://openalex.org/W4249365563","https://openalex.org/W4256186703"],"related_works":["https://openalex.org/W2393660303","https://openalex.org/W71446431","https://openalex.org/W2369014600","https://openalex.org/W2014443161","https://openalex.org/W2037739163","https://openalex.org/W4251679243","https://openalex.org/W3199192463","https://openalex.org/W2015411927","https://openalex.org/W2386833179","https://openalex.org/W2002233832"],"abstract_inverted_index":{"Let":[0],"f":[1,37],"be":[2,13,79],"a":[3,14,54,63,106],"not":[4],"necessarily":[5],"analytic":[6],"function":[7],"and":[8,33,102],"let":[9],"$A(":[10],"t":[11,41],")$":[12,43],"family":[15],"of":[16,30,36,56,72,84],"$n":[17],"\\times":[18],"n$":[19],"matrices":[20],"depending":[21],"on":[22],"the":[23,28,31,73,82,100],"parameter":[24],"t.":[25],"Conditions":[26],"for":[27,87],"existence":[29],"first":[32,74],"higher":[34],"derivatives":[35,52],"$f(":[38,57],"A":[39],"(":[40],")":[42],"are":[44,94,103],"presented":[45,92],"together":[46],"with":[47],"formulae":[48],"that":[49],"represent":[50],"these":[51],"as":[53],"submatrix":[55],"B":[58,61],")$,":[59],"where":[60],"is":[62,76],"larger":[64],"block":[65,69],"Toeplitz":[66],"matrix.":[67],"This":[68],"matrix":[70,88],"representation":[71],"derivative":[75],"shown":[77],"to":[78],"useful":[80],"in":[81,99,105],"context":[83],"condition":[85],"estimation":[86],"functions.":[89],"The":[90],"results":[91],"here":[93],"slightly":[95],"stronger":[96],"than":[97],"those":[98],"literature":[101],"proved":[104],"considerably":[107],"simpler":[108],"way.":[109]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":4}],"updated_date":"2026-03-06T13:50:29.536080","created_date":"2025-10-10T00:00:00"}