線性代數－精要與解析（原文書）（修訂版）

Ch1MATRICESANDVECTORS1-1MatricesandMatrixOperation1-2MatrixInverse;RulesofMatrixArithmetic1-3Norm(Length)andDotProduct1-4CrossProductCh2GENERALVECTORSPACES2-1RealVectorSpaces2-2Subspaces2-3LinearCombinationandSystemsofLinearEquations2-4LinearDependenceandLinearIndependence2-5BasisandDimensionCh3LINEARTRANSFORMATIONS3-1LinearTransformations3-2Range,Kernel,RankandNullity3-3MatricesofGeneralLinearTransformations3-4CompositionofLinearTransformationandMatrixMultiplication3-5InvertibillityandIsomorphisms3-6TheChangeofCoordinateMatrixCh4ELEMENTARYMATRIX4-1IntroductiontoSystemsofLinearEquations4-2GaussianElimination4-3ElementaryMatrixandElementaryOperationsCh5DETERMINANTS5-1DefinitionofDeterminantinPermutation(Option)5-2Determinantsof2*2Matrix5-3DefinitionandPropertiesoftheDeterminant5-4TheoremProofofDeterminant5-5Cramer`sRuleCh6INNERPRODUCTSPACES6-1InnerProductSpace6-2AngleandOrthogonalityinInnerProductSpaces6-3OrthonormalBases;Gram-SchmidtProcess;QR-Decomposition6-4BestApproximation:(LeastSquareMethod)6-5OrthogonalMatricesCh7EIGENVALUES,EIGENVECTORS7-1EigenvaluesandElgenvectors7-2Diagonalization7-3OrthogonalDiagonalizationCh8QUADRATICFORMS8-1QuadraticForms8-2DiagonalizingQuadraticForma;(ConicSections)8-3QuadricSurfacesCh9CANONICALFORM9-1JordanCanonicalForm

Ch1MATRICESANDVECTORS1-1MatricesandMatrixOperation1-2MatrixInverse;RulesofMatrixArithmetic1-3Norm(Length)andDotProduct1-4CrossProductCh2GENERALVECTORSPACES2-1RealVectorSpaces2-2Subspaces2-3LinearCombinationandSystemsofLinearEquations2-4LinearDependenceandLinearIndependence2-5BasisandDimensionCh3LINEARTRANSFORMATIONS3-1LinearTransformations3-2Range,Kernel,RankandNullity3-3MatricesofGeneralLinearTransformations3-4CompositionofLinearTransformationandMatrixMultiplication3-5InvertibillityandIsomorphi...