general linear group - Wiktionary

Usage notesEdit ... The general linear group can be denoted GL(n, F) or GLn(F) — or, if the field is understood, GL(n) or GLn. In the cases that F is the field of ... generallineargroup DefinitionfromWiktionary,thefreedictionary Jumptonavigation Jumptosearch Contents 1English 1.1Noun 1.1.1Usagenotes 1.1.2Derivedterms 1.1.3Relatedterms 1.1.4Translations 1.2Seealso 1.3Furtherreading English[edit] EnglishWikipediahasanarticleon:generallineargroupWikipedia Noun[edit] generallineargroup(pluralgenerallineargroups) (grouptheory)ForgivenfieldFandordern,thegroupofinvertiblen×nmatrices,withthegroupoperationofmatrixmultiplication. 1993,PeterJ.Olver,ApplicationsofLieGroupstoDifferentialEquations,Springer,2000,SoftcoverReprint,page17, OftenLiegroupsariseassubgroupsofcertainlargerLiegroups;forexample,theorthogonalgroupsaresubgroupsofthegenerallineargroupsofallinvertiblematrices. 2003,VladislavV.Goldberg(translator),MaksAizikovichAkivis,TensorCalculuswithApplications,WorldScientific,page119, WewillagaincallthisgroupthegenerallineargroupanddenoteitbyGL3. Injustthesameway,thesetofallnonsingularlineartransformationsoftheplaneL2isagroupdenotedbyGL2andcalledthegenerallineargroupofordertwo. 2009,RoeGoodman,NolanR.Wallach,Symmetry,Representations,andInvariants,Springer,page1, WeshowhowtoputaLiegroupstructureonaclosedsubgroupofthegenerallineargroupanddeterminetheLiealgebrasoftheclassicalgroups. Usagenotes[edit] ThegenerallineargroupcanbedenotedGL(n,F)orGLn(F)—or,ifthefieldisunderstood,GL(n)orGLn. InthecasesthatFisthefieldoftherealorofthecomplexnumbers,GL(n,F)isaLiegroup. Derivedterms[edit] projectivegenerallineargroup Relatedterms[edit] lineargroup Translations[edit] groupofinvertiblen×nmatrices Seealso[edit] Liegroup matrixgroup speciallineargroup Furtherreading[edit] GeneralsemilineargrouponWikipedia.Wikipedia MatrixgrouponWikipedia.Wikipedia ProjectivelineargrouponWikipedia.Wikipedia Retrievedfrom"https://en.wiktionary.org/w/index.php?title=general_linear_group&oldid=47658359" Categories:EnglishlemmasEnglishnounsEnglishcountablenounsEnglishmultiwordtermsen:Grouptheory Navigationmenu Personaltools NotloggedinTalkContributionsCreateaccountLogin Namespaces EntryDiscussion English Views ReadEditHistory More Search Navigation MainPageCommunityportalPreferencesRequestedentriesRecentchangesRandomentryHelpGlossaryDonationsContactus Tools WhatlinkshereRelatedchangesUploadfileSpecialpagesPermanentlinkPageinformationCitethispage Print/export CreateabookDownloadasPDFPrintableversion Inotherlanguages BahasaIndonesiaதமிழ்