matrix analysis and applied linear algebra (carl d meyer)

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1、ContentsPreface.......................ix1.LinearEquations..............11.1Introduction..................11.2GaussianEliminationandMatrices........31.3Gauss–JordanMethod..............151.4Two-PointBoundaryValueProblems.......181.5MakingGaussianEliminat

2、ionWork........211.6Ill-ConditionedSystems.............332.RectangularSystemsandEchelonForms...412.1RowEchelonFormandRank...........412.2ReducedRowEchelonForm...........472.3ConsistencyofLinearSystems..........532.4HomogeneousSystems..............572.5

3、NonhomogeneousSystems............642.6ElectricalCircuits................733.MatrixAlgebra..............793.1FromAncientChinatoArthurCayley.......793.2AdditionandTransposition...........813.3Linearity....................893.4WhyDoItThisWay..............

4、933.5MatrixMultiplication..............953.6PropertiesofMatrixMultiplication.......1053.7MatrixInversion...............1153.8InversesofSumsandSensitivity........1243.9ElementaryMatricesandEquivalence......1313.10TheLUFactorization.............1414.Vect

5、orSpaces...............1594.1SpacesandSubspaces.............1594.2FourFundamentalSubspaces..........1694.3LinearIndependence.............1814.4BasisandDimension.............194viContents4.5MoreaboutRank...............2104.6ClassicalLeastSquares........

6、....2234.7LinearTransformations............2384.8ChangeofBasisandSimilarity.........2514.9InvariantSubspaces..............2595.Norms,InnerProducts,andOrthogonality..2695.1VectorNorms................2695.2MatrixNorms................2795.3Inner-ProductSp

7、aces.............2865.4OrthogonalVectors..............2945.5Gram–SchmidtProcedure...........3075.6UnitaryandOrthogonalMatrices........3205.7OrthogonalReduction.............3415.8DiscreteFourierTransform...........3565.9ComplementarySubspaces...........

8、3835.10Range-NullspaceDecomposition........3945.11OrthogonalDecomposition...........4035.12SingularValueDecomposition.........4115.13OrthogonalProjection.............4295.14WhyLeastSquares?..............4465.15AnglesbetweenSubspaces....