Linear Algebra Through Geometry

LinearAlgebraThroughGeometryintroducestheconceptsoflinearalgebrathroughthecarefulstudyoftwoandthree-dimensionalEuclideangeometry.Thisapproachmakesitpossibletostartwithvectors,lineartransformations,andmatricesinthecontextoffamiliarplanegeometryandtomovedirectlytotopicssuchasdotproducts,determinants,eigenvalues,andquadraticforms.Thelaterchaptersdealwithn-dimensionalEuclideanspaceandotherfinite-dimensionalvectorspace.Topicsincludesystemsoflinearequationsinnvariable,innerproducts,symmetricmatrices,andquadraticforms.Thefinalchaptertreatsapplicationoflinearalgebratodifferentialsystems,leastsquareapproximationsandcurvatureofsurfacesinthreespaces.Theonlyprerequisiteforreadingthisbook(withtheexceptionofonesectiononsystemsofdifferentialequations)arehighschoolgeometry,algebra,andintroductorytrigonometry.Writtenfor»LowerundergraduateKeywords»Algebra-CON_D028-LineareAlgebraRelatedsubjects»Algebra-Geometry&Topology