MATRICESANDSYSTEMSOFLINEAREQUATIONS
1.1IntroductiontoMatricesandSystemsofLinearEquatio
1.2EchelonFormandGauss-JordanElimination
1.3Co istentSystemsofLinearEquatio
1.4Applicatio (Optional)
1.5MatrixOperatio
1.6AlgebraicPropertiesofMatrixOperatio
1.7LinearIndependenceandNo ingularMatrices
1.8DataFitting,NumericalIntegration,andNumericalDifferentiation(Optional)
1.9MatrixInve esandTheirProperties
VECTORSIN2-SPACEAND3-SPACE
2.1Vecto inthePlane
2.2Vecto inSpace
2.3TheDotProductandtheCrossProduct
2.4LinesandPlanesinSpace
THEVECTORSPACERn
3.1Introduction
3.2VectorSpacePropertiesofRn
3.3ExamplesofSubspaces
3.4BasesforSubspaces
3.5Dime ion
3.6OrthogonalBasesforSubspaces
3.7LinearTra formatio fromRntoRm
3.8Least-SquaresSolutio toInco istentSystems,withApplicatio toDataFitting
3.9TheoryandPracticeofLeastSquares
THEEIGENVALUEPROBLEM
4.1TheEigenvalueProblemfor(2x2)Matrices
4.2DeterminantsandtheEigenvalueProblem
4.3ElementaryOperatio andDeterminants(Optional)
4.4EigenvaluesandtheCharacteristicPolynomial
4.5Eigenvecto andEige paces
4.6ComplexEigenvaluesandEigenvecto
4.7SimilarityTra formatio andDiagonalization
4.8DifferenceEquatio ;MarkovChai ;SystemsofDifferentialEquatio (Optional)
VECTORSPACESANDLINEARTRANSFORMATIONS
5.1Introduction
5.2VectorSpaces
5.3Subspaces
5.4LinearIndependence,Bases,andCoordinates
5.5Dime ion
5.6Inner-ProductSpaces,OrthogonalBases,andProjectio (Optional)
5.7LinearTra formatio
5.8Operatio withLinearTra formatio
5.9MatrixRepresentatio forLinearTra formatio
5.10ChangeofBasisandDiagonalization
DETERMINANTS
6.1Introduction
6.2CofactorExpa io ofDeterminants
6.3ElementaryOperatio andDeterminants
6.4Cramer'sRule
6.5Applicatio ofDeterminants:Inve esandWronksia
EIGENVALUESANDAPPLICATIONS
7.1QuadraticForms
7.2SystemsofDifferentialEquatio
7.3Tra formationtoHessenbergForm
7.4EigenvaluesofHessenbergMatrices
7.5HouseholderTra formatio
7.6TheQRFactorizationandLeast-SquaresSolutio
7.7MatrixPolynomialsandtheCayley-HamiltonTheorem
7.8GeneralizedEigenvecto andSolutio ofSystemsofDifferentialEquatio
APPENDIX:ANINTRODUCTIONTOMATLAB
ANSWERSTOSELECTEDODD-NUMBEREDEXERCISES
INDEX