General Linear Group -- from Wolfram MathWorld

Given a ring R with identity, the general linear group GL_n(R) is the group of n×n invertible matrices with elements in R. The general linear group GL_n(q) ... Algebra AppliedMathematics CalculusandAnalysis DiscreteMathematics FoundationsofMathematics Geometry HistoryandTerminology NumberTheory ProbabilityandStatistics RecreationalMathematics Topology AlphabeticalIndex NewinMathWorld Algebra GroupTheory FiniteGroups Algebra GroupTheory MatrixGroups MathWorldContributors Terr GeneralLinearGroup Givenaringwithidentity,thegenerallineargroup isthegroupofinvertible matriceswithelementsin. Thegenerallineargroupistheset ofmatrices withentriesinthefieldwhichhavenonzerodeterminant. SeealsoLanglandsReciprocity,ProjectiveGeneralLinearGroup, ProjectiveSpecialLinearGroup, SpecialLinearGroup PortionsofthisentrycontributedbyDavid Terr ExplorewithWolfram|Alpha Morethingstotry: finitegroups {{2,-1,1},{0,-2,1},{1,-2,0}}.{x,y,z} ellipsewithequation(x-2)^2/25+(y+1)^2/10=1 ReferencesConway,J. H.;Curtis,R. T.;Norton,S. P.;Parker,R. A.;andWilson,R. A."TheGroups,,,and."§2.1inAtlas ofFiniteGroups:MaximalSubgroupsandOrdinaryCharactersforSimpleGroups. Oxford,England:ClarendonPress,p. x,1985.ReferencedonWolfram|AlphaGeneralLinearGroup Citethisas: Terr,DavidandWeisstein,EricW."GeneralLinearGroup."FromMathWorld--A WolframWebResource.https://mathworld.wolfram.com/GeneralLinearGroup.html Subjectclassifications Algebra GroupTheory FiniteGroups Algebra GroupTheory MatrixGroups MathWorldContributors Terr Created,developedandnurturedbyEricWeissteinatWolframResearch