MIT 18.06SC Linear Algebra, Fall 2011 (English)

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Lecture 1: An Interview with Gilbert Strang on Teaching Linear Algebra

Lecture 2: Course Introduction | MIT 18.06SC Linear Algebra

Lecture 3: 1. The Geometry of Linear Equations

Lecture 4: Geometry of Linear Algebra

Lecture 5: Rec 1 | MIT 18.085 Computational Science and Engineering I, Fall 2008

Lecture 6: An Overview of Key Ideas

Lecture 7: 2. Elimination with Matrices.

Lecture 8: Elimination with Matrices

Lecture 9: 3. Multiplication and Inverse Matrices

Lecture 10: Inverse Matrices

Lecture 11: 4. Factorization into A = LU

Lecture 12: LU Decomposition

Lecture 13: 5. Transposes, Permutations, Spaces R^n

Lecture 14: Subspaces of Three Dimensional Space

Lecture 15: 6. Column Space and Nullspace

Lecture 16: Vector Subspaces

Lecture 17: 7. Solving Ax = 0: Pivot Variables, Special Solutions

Lecture 18: Solving Ax=0

Lecture 19: 8. Solving Ax = b: Row Reduced Form R

Lecture 20: Solving Ax=b

Lecture 21: 9. Independence, Basis, and Dimension

Lecture 22: Basis and Dimension

Lecture 23: 10. The Four Fundamental Subspaces

Lecture 24: Computing the Four Fundamental Subspaces

Lecture 25: 11. Matrix Spaces; Rank 1; Small World Graphs

Lecture 26: Matrix Spaces

Lecture 27: 12. Graphs, Networks, Incidence Matrices

Lecture 28: Graphs and Networks

Lecture 29: 13. Quiz 1 Review

Lecture 30: Exam #1 Problem Solving

Lecture 31: 14. Orthogonal Vectors and Subspaces

Lecture 32: Orthogonal Vectors and Subspaces

Lecture 33: 15. Projections onto Subspaces

Lecture 34: Projection into Subspaces

Lecture 35: 16. Projection Matrices and Least Squares

Lecture 36: Least Squares Approximation

Lecture 37: 17. Orthogonal Matrices and Gram-Schmidt

Lecture 38: Gram-Schmidt Orthogonalization

Lecture 39: 18. Properties of Determinants

Lecture 40: Properties of Determinants

Lecture 41: 19. Determinant Formulas and Cofactors

Lecture 42: Determinants

Lecture 43: 20. Cramer's Rule, Inverse Matrix, and Volume

Lecture 44: Determinants and Volume

Lecture 45: 21. Eigenvalues and Eigenvectors

Lecture 46: Eigenvalues and Eigenvectors

Lecture 47: 22. Diagonalization and Powers of A

Lecture 48: Powers of a Matrix

Lecture 49: 23. Differential Equations and exp(At)

Lecture 50: Differential Equations and exp (At)

Lecture 51: 24. Markov Matrices; Fourier Series

Lecture 52: Markov Matrices

Lecture 53: 24b. Quiz 2 Review

Lecture 54: Exam #2 Problem Solving

Lecture 55: 25. Symmetric Matrices and Positive Definiteness

Lecture 56: Symmetric Matrices and Positive Definiteness

Lecture 57: 26. Complex Matrices; Fast Fourier Transform

Lecture 58: Complex Matrices

Lecture 59: 27. Positive Definite Matrices and Minima

Lecture 60: Positive Definite Matrices and Minima

Lecture 61: 28. Similar Matrices and Jordan Form

Lecture 62: Similar Matrices

Lecture 63: 29. Singular Value Decomposition

Lecture 64: Computing the Singular Value Decomposition

Lecture 65: 30. Linear Transformations and Their Matrices

Lecture 66: Linear Transformations

Lecture 67: 31. Change of Basis; Image Compression

Lecture 68: Change of Basis

Lecture 69: 33. Left and Right Inverses; Pseudoinverse

Lecture 70: Pseudoinverses

Lecture 71: 32. Quiz 3 Review

Lecture 72: Exam #3 Problem Solving

Lecture 73: 34. Final Course Review

Lecture 74: Final Exam Problem Solving