麻省理工開放課程：線性代數 Linear Algebra 英文版 DVD 只於電腦播放

課程介紹：
這個基礎課程主要闡述矩陣理論和線性代數。主題重點放在對在其他學科的有用的法則上面，包括方程組，向量空間，行列式，特徵值，相似性，以及正定矩陣。

導師介紹
GilbertStrangwasanundergraduateatMITandaRhodesScholaratBalliolCollege,Oxford.HisPh.D.wasfromUCLAandsincethenhehastaughtatMIT.HehasbeenaSloanFellowandaFairchildScholarandisaFellowoftheAmericanAcademyofArtsandSciences.HeisaProfessorofMathematicsatMITandanHonoraryFellowofBalliolCollege.
HewasthePresidentofSIAMduring1999and2000,andChairoftheJointPolicyBoardforMathematics.HereceivedthevonNeumannMedaloftheUSAssociationforComputationalMechanics,andtheHenriciPrizeforappliedanalysis.ThefirstSuBuchinPrizefromtheInternationalCongressofIndustrialandAppliedMathematics,andtheHaimoPrizefromtheMathematicalAssociationofAmerica,wereawardedforhiscontributionstoteachingaroundtheworld.Hishomepageismath.mit.edu/~gs/andhisvideolecturesonlinearalgebraandoncomputationalscienceandengineeringareonocw.mit.edu(mathematics/18.06and18.085).
目錄:


Lecture01:TheGeometryofLinearEquations
Lecture02:EliminationwithMatrices
Lecture03:MultiplicationandInverseMatrices
Lecture04:FactorizationintoA=LU
Lecture05:Transposes,Permutations,SpacesR^n
Lecture06:ColumnSpaceandNullspace
Lecture07:SolvingAx=0:PivotVariables,SpecialSolutions
Lecture08:SolvingAx=b:RowReducedFormR
Lecture09:Independence,Basis,andDimension
Lecture10:TheFourFundamentalSubspaces
Lecture11:MatrixSpaces;Rank1;SmallWorldGraphs
Lecture12:Graphs,Networks,IncidenceMatrices
Lecture13:Quiz1Review
Lecture14:OrthogonalVectorsandSubspaces
Lecture15:ProjectionsontoSubspaces
Lecture16:ProjectionMatricesandLeastSquares
Lecture17:OrthogonalMatricesandGram-Schmidt
Lecture18:PropertiesofDeterminants
Lecture19:DeterminantFormulasandCofactors
Lecture20:Cramer'sRule,InverseMatrix,andVolume
Lecture21:EigenvaluesandEigenvectors
Lecture22:DiagonalizationandPowersofA
Lecture23:DifferentialEquationsandexp(At)
Lecture24:MarkovMatrices;FourierSeries
Lecture24b:Quiz2Review
Lecture25:SymmetricMatricesandPositiveDefiniteness
Lecture26:ComplexMatrices;FastFourierTransform
Lecture27:PositiveDefiniteMatricesandMinimae
Lecture28:SimilarMatricesandJordanForm
Lecture29:SingularValueDecomposition
Lecture30:LinearTransformationsandTheirMatrices
Lecture31:ChangeofBasis;ImageCompression
Lecture32:Quiz3Review
Lecture33:LeftandRightInverses;Pseudoinverse
Lecture34:FinalCourseReview