linear_algebra_and_its_applications_4ed_gilbert_strang_[线性代数及其应用]

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1、LinearAlgebraandItsApplicationsFourthEditionGilbertStrangx;y)zAx;byAy;bb0zAz;00ContentsPrefaceiv1MatricesandGaussianElimination11.1Introduction................................11.2TheGeometryofLinearEquations....................41.3AnExampleofGaussianElimination..................131.4MatrixNota

2、tionandMatrixMultiplication................211.5TriangularFactorsandRowExchanges.................361.6InversesandTransposes..........................501.7SpecialMatricesandApplications....................66ReviewExercises.............................722VectorSpaces772.1VectorSpacesandSubspaces

3、.......................772.2SolvingAx=0andAx=b........................862.3LinearIndependence,Basis,andDimension...............1032.4TheFourFundamentalSubspaces....................1152.5GraphsandNetworks...........................1292.6LinearTransformations..........................140ReviewEx

4、ercises.............................1543Orthogonality1593.1OrthogonalVectorsandSubspaces....................1593.2CosinesandProjectionsontoLines....................1713.3ProjectionsandLeastSquares......................1803.4OrthogonalBasesandGram-Schmidt..................1953.5TheFastFourierTr

5、ansform........................211ReviewExercises.............................221iiiCONTENTS4Determinants2254.1Introduction................................2254.2PropertiesoftheDeterminant.......................2274.3FormulasfortheDeterminant.......................2364.4ApplicationsofDeterminan

6、ts.......................247ReviewExercises.............................2585EigenvaluesandEigenvectors2605.1Introduction................................2605.2DiagonalizationofaMatrix........................2735.3DifferenceEquationsandPowersAk...................2835.4DifferentialEquationsandeAt

7、......................2965.5ComplexMatrices.............................3125.6SimilarityTransformations........................325ReviewExercises.............................3416PositiveDefiniteMatrices3456.1Minima,Maxima,andSaddlePoints