Linear_Algebra_and_Its_Applications_4_Gilbert_Strang英文电子资料.pdf

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1、LinearAlgebraandItsApplicationsFourthEditionGilbertStrangx;y)zAx;byAy;bb0zAz;00ContentsPrefaceiv1MatricesandGaussianElimination11.1Introduction................................11.2TheGeometryofLinearEquations....................41.3AnExampleofGaussianElimination..................131.

2、4MatrixNotationandMatrixMultiplication................211.5TriangularFactorsandRowExchanges.................361.6InversesandTransposes..........................501.7SpecialMatricesandApplications....................66ReviewExercises.............................722VectorSpaces772.1Ve

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

4、......................140ReviewExercises.............................1543Orthogonality1593.1OrthogonalVectorsandSubspaces....................1593.2CosinesandProjectionsontoLines....................1713.3ProjectionsandLeastSquares......................1803.4OrthogonalBasesandGram-Sch

5、midt..................1953.5TheFastFourierTransform........................211ReviewExercises.............................221iiiCONTENTS4Determinants2254.1Introduction................................2254.2PropertiesoftheDeterminant.......................2274.3FormulasfortheDetermina

6、nt.......................2364.4ApplicationsofDeterminants.......................247ReviewExercises.............................2585EigenvaluesandEigenvectors2605.1Introduction................................2605.2DiagonalizationofaMatrix........................2735.3DifferenceEquati

7、onsandPowersAk...................2835.4DifferentialEquationsandeAt......................2965.5ComplexMatrices.............................3125.6SimilarityTransformations........................325ReviewExercises.............................3416PositiveDefiniteMatrices3456.1Minima,Max

8、ima,andSaddlePoints