Linear_Algebra_and_Its_Applications_4ed_Gilbert_Strang_[线性代数及其应用].pdf

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1、LinearAlgebraandItsApplicationsFourthEditionGilbertStrangxyz;)Ax;byAy;bb0zAz;00ContentsPrefaceiv1MatricesandGaussianElimination11.1Introduction................................11.2TheGeometryofLinearEquations....................41.3AnExampleofGaussianEliminatio

2、n..................131.4MatrixNotationandMatrixMultiplication................211.5TriangularFactorsandRowExchanges.................361.6InversesandTransposes..........................501.7SpecialMatricesandApplications....................66ReviewExercises.....

3、........................722VectorSpaces772.1VectorSpacesandSubspaces.......................772.2SolvingAx=0andAx=b........................862.3LinearIndependence,Basis,andDimension...............1032.4TheFourFundamentalSubspaces....................1152.5Graphs

4、andNetworks...........................1292.6LinearTransformations..........................140ReviewExercises.............................1543Orthogonality1593.1OrthogonalVectorsandSubspaces....................1593.2CosinesandProjectionsontoLines..............

5、......1713.3ProjectionsandLeastSquares......................1803.4OrthogonalBasesandGram-Schmidt..................1953.5TheFastFourierTransform........................211ReviewExercises.............................221iiiCONTENTS4Determinants2254.1Introduction.

6、...............................2254.2PropertiesoftheDeterminant.......................2274.3FormulasfortheDeterminant.......................2364.4ApplicationsofDeterminants.......................247ReviewExercises.............................2585Eigenvaluesand

7、Eigenvectors2605.1Introduction................................2605.2DiagonalizationofaMatrix........................2735.3DifferenceEquationsandPowersAk...................2835.4DifferentialEquationsandeAt......................2965.5ComplexMatrices.............

8、................3125.6SimilarityTransformations........................325ReviewExercises.............................3416PositiveDefiniteMatrices3456.1Minima,Maxima,andSaddlePoints