矩阵理论_Matrix_Theory .pdf

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1、TABLEOFCONTENTS1.LinearEquations................11.1Introduction.........................11.2GaussianEliminationandMatrices.............31.3Gauss–JordanMethod..................151.4Two-PointBoundaryValueProblems...........181.5MakingGaussianEliminationWork............211.6Ill-ConditionedSystems...

2、...............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.

4、...........1053.7MatrixInversion.....................1153.8InversesofSumsandSensitivity..............1243.9ElementaryMatricesandEquivalence...........1313.10TheLUFactorization..................1414.VectorSpaces.................1594.1SpacesandSubspaces...................1594.2FourFundamentalSubspac

5、es...............1694.3LinearIndependence...................1814.4BasisandDimension...................1944.5MoreaboutRank.....................2104.6ClassicalLeastSquares..................2214.7LinearTransformations..................2364.8ChangeofBasisandSimilarity..............2494.9InvariantSubsp

6、aces....................2575.Norms,InnerProducts,andOrthogonality....2675.1VectorNorms.......................2675.2MatrixNorms.......................2775.3Inner-ProductSpaces...................2845.4OrthogonalVectors....................2925.5Gram–SchmidtProcedure.................3065.6UnitaryandOr

7、thogonalMatrices.............3195.7OrthogonalReduction...................3405.8DiscreteFourierTransform................3555.9ComplementarySubspaces................3825.10Range-NullspaceDecomposition.............3