Matrix Analysis.pdf

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1、ContentsPreface.......................ix1.LinearEquations..............11.1Introduction..................11.2GaussianEliminationandMatrices........31.3Gauss–JordanMethod..............151.4Two-PointBoundaryValueProblems.......181.5MakingGaussianEliminationWork........211.6Ill-Conditio

2、nedSystems.............332.RectangularSystemsandEchelonForms...412.1RowEchelonFormandRank...........412.2ReducedRowEchelonForm...........472.3ConsistencyofLinearSystems..........532.4HomogeneousSystems..............572.5NonhomogeneousSystems............642.6ElectricalCircuits........

3、........733.MatrixAlgebra..............793.1FromAncientChinatoArthurCayley.......793.2AdditionandTransposition...........813.3Linearity....................893.4WhyDoItThisWay..............933.5MatrixMultiplication..............953.6PropertiesofMatrixMultiplication.......1053.7MatrixI

4、nversion...............1153.8InversesofSumsandSensitivity........1243.9ElementaryMatricesandEquivalence......1313.10TheLUFactorization.............1414.VectorSpaces...............1594.1SpacesandSubspaces.............1594.2FourFundamentalSubspaces..........1694.3LinearIndependence....

5、.........1814.4BasisandDimension.............194viContents4.5MoreaboutRank...............2104.6ClassicalLeastSquares............2234.7LinearTransformations............2384.8ChangeofBasisandSimilarity.........2514.9InvariantSubspaces..............2595.Norms,InnerProducts,andOrthogonal

6、ity..2695.1VectorNorms................2695.2MatrixNorms................2795.3Inner-ProductSpaces.............2865.4OrthogonalVectors..............2945.5Gram–SchmidtProcedure...........3075.6UnitaryandOrthogonalMatrices........3205.7OrthogonalReduction.............3415.8DiscreteFourie

7、rTransform...........3565.9ComplementarySubspaces...........3835.10Range-NullspaceDecomposition........3945.11OrthogonalDecomposition...........4035.12SingularValueDecomposition.........4115.13OrthogonalProjection.............4295.14WhyLeastSquares?..............4465.15AnglesbetweenS

8、ubspaces....