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1、LinearAlgebraandItsApplicationsFourthEditionGilbertStrangx?y)zAx?byAy?bb0zAz?00ContentsPrefaceiv1MatricesandGaussianElimination11.1Introduction................................11.2TheGeometryofLinearEquations....................41.3AnExampleofGaussianElimination..................131.4MatrixNotati
2、onandMatrixMultiplication................211.5TriangularFactorsandRowExchanges.................361.6InversesandTransposes..........................501.7SpecialMatricesandApplications....................66ReviewExercises.............................722VectorSpaces772.1VectorSpacesandSubspaces....
3、...................772.2SolvingAx=0andAx=b........................862.3LinearIndependence,Basis,andDimension...............1032.4TheFourFundamentalSubspaces....................1152.5GraphsandNetworks...........................1292.6LinearTransformations..........................140ReviewExercise
4、s.............................1543Orthogonality1593.1OrthogonalVectorsandSubspaces....................1593.2CosinesandProjectionsontoLines....................1713.3ProjectionsandLeastSquares......................1803.4OrthogonalBasesandGram-Schmidt..................1953.5TheFastFourierTransform.
5、.......................211ReviewExercises.............................221iiiCONTENTS4Determinants2254.1Introduction................................2254.2PropertiesoftheDeterminant.......................2274.3FormulasfortheDeterminant.......................2364.4ApplicationsofDeterminants........
6、...............247ReviewExercises.............................2585EigenvaluesandEigenvectors2605.1Introduction................................2605.2DiagonalizationofaMatrix........................2735.3DifferenceEquationsandPowersAk...................2835.4DifferentialEquationsandeAt............
7、..........2965.5ComplexMatrices.............................3125.6SimilarityTransformations........................325ReviewExercises.............................3416PositiveDe?niteMatrices3456.1Minima,Maxima,andSaddlePoints
