A trigonometric identity for 2 × 2 block matrices
This note extends some formulas relating exponential, trigonometric and hyperbolic trigonometric functions to a subset of 2 × 2 block matrices.
Saved in:
| Published in: | International journal of mathematical education in science and technology Vol. 46; no. 6; pp. 921 - 925 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
London
Taylor & Francis
18.08.2015
Taylor & Francis Ltd |
| Subjects: | |
| ISSN: | 0020-739X, 1464-5211 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | This note extends some formulas relating exponential, trigonometric and hyperbolic trigonometric functions to a subset of 2 × 2 block matrices. |
|---|---|
| AbstractList | This note extends some formulas relating exponential, trigonometric and hyperbolic trigonometric functions to a subset of 2 × 2 block matrices. |
| Author | Withers, Christopher S. Nadarajah, Saralees |
| Author_xml | – sequence: 1 givenname: Christopher S. surname: Withers fullname: Withers, Christopher S. organization: Applied Mathematics Group, Industrial Research Limited – sequence: 2 givenname: Saralees surname: Nadarajah fullname: Nadarajah, Saralees email: mbbsssn2@manchester.ac.uk organization: School of Mathematics, University of Manchester |
| BookMark | eNp9kMlKA0EQhhuJYBJ9BGHA88TqZSbTN0NwA8GLgremV5k40x27J0iexAfyxewh8eqlqii-v5Z_hiY-eIvQJYYFhgauAQgsKX9bEMBVbmHGGT1BU8xqVlYE4wmajkw5QmdoltIGIFOMTxFZFUNs34MPvc2FLlpj_dAO-8KFWJDi5zsH1QX9UfRyBGw6R6dOdsleHPMcvd7dvqwfyqfn-8f16qnU-Y6h5A1IzRtnlNNKU461YbVjlWyY0aTWYJWRtaQUnF4CMcRiVzFlrOZOWQV0jq4Oc7cxfO5sGsQm7KLPKwWuOTCKMaGZqg6UjiGlaJ3YxraXcS8wiNEe8WePGO0RR3uy7uaga33-tJdfIXZGDHLfheii9LpNgv4_4hfgaG4Y |
| CODEN | IJMEBM |
| Cites_doi | 10.1080/00207390116735 10.1080/00207390117381 |
| ContentType | Journal Article |
| Copyright | 2015 Taylor & Francis 2015 2015 Taylor & Francis |
| Copyright_xml | – notice: 2015 Taylor & Francis 2015 – notice: 2015 Taylor & Francis |
| DBID | AAYXX CITATION AHOVV |
| DOI | 10.1080/0020739X.2015.1014943 |
| DatabaseName | CrossRef Education Research Index |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1464-5211 |
| EndPage | 925 |
| ExternalDocumentID | 3723079321 10_1080_0020739X_2015_1014943 1014943 |
| Genre | Classroom notes General Information |
| GroupedDBID | -~X .7F .DC .GO .QJ 0BK 0R~ 186 29J 30N 4.4 5GY 5VS 85S AAENE AAGDL AAHIA AAHSB AAJMT AALDU AAMIU AAPUL AAQRR ABCCY ABFIM ABHAV ABJNI ABLIJ ABPAQ ABPEM ABPPZ ABTAI ABUFD ABXUL ABXYU ACGEJ ACGFS ACIWK ACTIO ADCVX ADGTB ADMHC ADXPE AEISY AEOZL AEPSL AEYOC AFKVX AFRVT AGDLA AGMYJ AHDZW AIJEM AIYEW AJWEG AKBVH AKOOK ALMA_UNASSIGNED_HOLDINGS ALQZU AMVHM AQRUH AQTUD AVBZW AWYRJ BLEHA CCCUG CE4 CS3 D0L DGEBU DKSSO EBS EJD E~A E~B GTTXZ H13 HF~ HZ~ H~P IPNFZ J.P KYCEM M4Z NA5 NY~ O9- P2P PQQKQ RIG RNANH ROSJB RTWRZ S-T SNACF TASJS TBQAZ TDBHL TEJ TFL TFT TFW TTHFI TUROJ TWF UT5 UU3 WH7 ZGOLN ~S~ AAYXX CITATION AHOVV |
| ID | FETCH-LOGICAL-c201t-980ac98fdbfcbc391cd46f45a84dc26c0ebda6a330fc702d2e1f54bdec9fbeb03 |
| IEDL.DBID | TFW |
| ISSN | 0020-739X |
| IngestDate | Sun Jul 27 14:45:36 EDT 2025 Sat Nov 29 05:33:53 EST 2025 Mon Oct 20 23:45:09 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 6 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c201t-980ac98fdbfcbc391cd46f45a84dc26c0ebda6a330fc702d2e1f54bdec9fbeb03 |
| Notes | SourceType-Scholarly Journals-1 ObjectType-General Information-1 content type line 14 |
| PQID | 1690431123 |
| PQPubID | 176146 |
| PageCount | 5 |
| ParticipantIDs | crossref_primary_10_1080_0020739X_2015_1014943 informaworld_taylorfrancis_310_1080_0020739X_2015_1014943 proquest_journals_1690431123 |
| PublicationCentury | 2000 |
| PublicationDate | 2015-08-18 |
| PublicationDateYYYYMMDD | 2015-08-18 |
| PublicationDate_xml | – month: 08 year: 2015 text: 2015-08-18 day: 18 |
| PublicationDecade | 2010 |
| PublicationPlace | London |
| PublicationPlace_xml | – name: London |
| PublicationTitle | International journal of mathematical education in science and technology |
| PublicationYear | 2015 |
| Publisher | Taylor & Francis Taylor & Francis Ltd |
| Publisher_xml | – name: Taylor & Francis – name: Taylor & Francis Ltd |
| References | cit0001 Halmos PR (cit0004) 1958 Withers CS (cit0003) 2008; 38 cit0002 |
| References_xml | – volume-title: Finite dimensional vector spaces year: 1958 ident: cit0004 – ident: cit0001 doi: 10.1080/00207390116735 – ident: cit0002 doi: 10.1080/00207390117381 – volume: 38 start-page: 171 year: 2008 ident: cit0003 publication-title: N Z J Math. |
| SSID | ssj0001449 |
| Score | 1.9663342 |
| Snippet | This note extends some formulas relating exponential, trigonometric and hyperbolic trigonometric functions to a subset of 2 × 2 block matrices. |
| SourceID | proquest crossref informaworld |
| SourceType | Aggregation Database Index Database Publisher |
| StartPage | 921 |
| SubjectTerms | block matrices Jordan normal form trigonometric and hyperbolic matrix functions and identities |
| Title | A trigonometric identity for 2 × 2 block matrices |
| URI | https://www.tandfonline.com/doi/abs/10.1080/0020739X.2015.1014943 https://www.proquest.com/docview/1690431123 |
| Volume | 46 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAWR databaseName: Taylor & Francis Journals customDbUrl: eissn: 1464-5211 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001449 issn: 0020-739X databaseCode: TFW dateStart: 19700101 isFulltext: true titleUrlDefault: https://www.tandfonline.com providerName: Taylor & Francis |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LSwMxEA5SPOjBt1itkoPXSDabzW6ORSxeLB4q9hbyhCJW6a6Cv8Qf5B8zs49iEfGgl0AOmQ2zmVcy8w1C5zzkTNssJ1bmMUBxzBEtUkMynQgfBUwbZ-pmE_l4XEyn8rbNJizbtEqIoUMDFFHrahBubcouIw4quOF9aQqJWRmEn1xywPuMph96GExG90tdHMOFNsmDEljS1fD8RGXFOq1gl37T1bUBGm3_w9Z30FbrfeJhc1x20Zqf76HNmyV0a7mP2BBXMWKHWgdotmXxrCnlfcNxl5jhj_c4mGgCH_BjDe_vywN0N7qaXF6TtrECsfG7FZEF1VYWwZlgjU1lYh0XgWe64M4yYak3TgudpjTYnDLHfBIybpy3MhhvaHqIevOnuT9CWDhAVONGcBfF32WRqLPcR6_HpMxR3UcXHUPVc4OfoZIlLGnDDAXMUC0z-kh-Zbuq6ouL0HQZUekvawfdP1KtKJYK3gGjlxQt9PEfSJ-gDZjCbXJSDFCvWrz4U7RuX6tZuTirD90nLmXUFA |
| linkProvider | Taylor & Francis |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LSwMxEA5aBfXgW6xWzcHrym6SfeRYxFKx7alibyFPKGKV7ir4S_xB_jEzu9vSIuJBL3tZMhtm55nMfIPQJXMpkTpOA81Tn6AYYgKZUBXEMkqsVzCpjCqHTaSDQTYa8cVeGCirhBzaVUARpa0G5YbD6FlJHLRwwwXTCCqzYsg_GWd0Fa3F3teClA87D3Nr7BOGuswjDGDNrIvnJzJL_mkJvfSbtS5dUGfnPza_i7brABS3K4nZQyt2so-2-nP01vwAkTYufNIO7Q4wb0vjcdXN-479NjHBnx_-obwXfMRPJcK_zQ_RfedmeN0N6tkKgfbfLQKehVLzzBnltNKUR9qwxLFYZsxokujQKiMTSWnodBoSQ2zkYqaM1dwpq0J6hBqT54k9RjgxAKrGVMKMtwAm9kSNZtYHPooSE8omuppxVLxUEBoimiOTVswQwAxRM6OJ-CLfRVGeXbhq0Iigv6xtzX6SqLUxF3AV6AMl76RP_kD6Am10h_2e6N0O7k7RJryCw-Uoa6FGMX21Z2hdvxXjfHpeSuAXsiPYPw |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LS8QwEA66iujBt7i6ag5eK22Sps1xUYuiLntYcW8hT1jEddlWwV_iD_KPmfSxuIh40EsvJdMwzWTmS2a-AeCU2AQJFSeBYokDKBrpQFAsg1hE1DgDE1LLstlE0uulwyHr19mEeZ1W6TG0rYgiyr3aG_dE2yYjzldw-_uloU_Mij38JIzgRbDkQmfq8dcge5htxg4v1FkeYeDHNEU8P4mZc09z5KXfNuvSA2Ub_zD3TbBeh5-wW62XLbBgxttg7W7G3ZrvANSFhYPsvtjBd9tScFTV8r5BN0uI4Me7e0jnAx_hU8nvb_JdcJ9dDs6vgrqzQqDcd4uApaFQLLVaWiUVZpHShFoSi5RohagKjdSCCoxDq5IQaWQiGxOpjWJWGhniPdAaP4_NPoBUe0o1IinRzv517IRqRYwLeyRGOhRtcNYolE8qAg0ezXhJK2VwrwxeK6MN2Fe186I8ubBVmxGOfxnbaf4Rr20x5_4i0IVJzkUf_EH0CVjpX2T89rp3cwhW_Rt_shylHdAqpi_mCCyr12KUT4_L9fcJQQHW8A |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+trigonometric+identity+for+2+%C3%97+2+block+matrices&rft.jtitle=International+journal+of+mathematical+education+in+science+and+technology&rft.au=Withers%2C+Christopher+S.&rft.au=Nadarajah%2C+Saralees&rft.date=2015-08-18&rft.pub=Taylor+%26+Francis&rft.issn=0020-739X&rft.eissn=1464-5211&rft.volume=46&rft.issue=6&rft.spage=921&rft.epage=925&rft_id=info:doi/10.1080%2F0020739X.2015.1014943&rft.externalDocID=1014943 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0020-739X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0020-739X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0020-739X&client=summon |