1 An Interview with Gilbert Strang on Teaching Linear Algebra 2 Course Introduction | MIT 18.06SC Linear Algebra 3 1. The Geometry of Linear Equations 4 Geometry of Linear Algebra 5 Rec 1 | MIT 18.085 Computational Science and Engineering I, Fall 2008 6 An Overview of Key Ideas 7 2. Elimination with Matrices. 8 Elimination with Matrices 9 3. Multiplication and Inverse Matrices 10 Inverse Matrices 11 4. Factorization into A = LU 12 LU Decomposition 13 5. Transposes, Permutations, Spaces R^n 14 Subspaces of Three Dimensional Space 15 6. Column Space and Nullspace 16 Vector Subspaces 17 7. Solving Ax = 0: Pivot Variables, Special Solutions 18 Solving Ax=0 19 8. Solving Ax = b: Row Reduced Form R 20 Solving Ax=b 21 9. Independence, Basis, and Dimension 22 Basis and Dimension 23 10. The Four Fundamental Subspaces 24 Computing the Four Fundamental Subspaces 25 11. Matrix Spaces; Rank 1; Small World Graphs 26 Matrix Spaces 27 12. Graphs, Networks, Incidence Matrices 28 Graphs and Networks 29 13. Quiz 1 Review 30 Exam #1 Problem Solving 31 14. Orthogonal Vectors and Subspaces 32 Orthogonal Vectors and Subspaces 33 15. Projections onto Subspaces 34 Projection into Subspaces 35 16. Projection Matrices and Least Squares 36 Least Squares Approximation 37 17. Orthogonal Matrices and Gram-Schmidt 38 Gram-Schmidt Orthogonalization 39 18. Properties of Determinants 40 Properties of Determinants 41 19. Determinant Formulas and Cofactors 42 Determinants 43 20. Cramer's Rule, Inverse Matrix, and Volume 44 Determinants and Volume 45 21. Eigenvalues and Eigenvectors 46 Eigenvalues and Eigenvectors 47 22. Diagonalization and Powers of A 48 Powers of a Matrix 49 23. Differential Equations and exp(At) 50 Differential Equations and exp (At) 51 24. Markov Matrices; Fourier Series 52 Markov Matrices 53 24b. Quiz 2 Review 54 Exam #2 Problem Solving 55 25. Symmetric Matrices and Positive Definiteness 56 Symmetric Matrices and Positive Definiteness 57 26. Complex Matrices; Fast Fourier Transform 58 Complex Matrices 59 27. Positive Definite Matrices and Minima 60 Positive Definite Matrices and Minima 61 28. Similar Matrices and Jordan Form 62 Similar Matrices 63 29. Singular Value Decomposition 64 Computing the Singular Value Decomposition 65 30. Linear Transformations and Their Matrices 66 Linear Transformations 67 31. Change of Basis; Image Compression 68 Change of Basis 69 33. Left and Right Inverses; Pseudoinverse 70 Pseudoinverses 71 32. Quiz 3 Review 72 Exam #3 Problem Solving 73 34. Final Course Review 74 Final Exam Problem Solving