MIT 18.06SC Linear Algebra, Fall 2011
Instructor: Gilbert Strang
The Help Session Videos were developed by: Martina Balagovic, Linan Chen, Benjamin Harris, Ana Rita Pires, David Shirokoff, Nikola Kamburov
View the complete course: http://ocw.mit.edu/18-06SCF11
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Curated by: MIT OpenCourseWare (74 videos)
Currently Playing: Rec 1 | MIT 18.085 Computational Science and Engineering I, Fall 2008
Recitation 1: Key ideas of linear algebra
License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
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Tracks in this Playlist
- An Interview with Gilbert Strang on Teaching Linear Algebra
- Course Introduction | MIT 18.06SC Linear Algebra
- 1. The Geometry of Linear Equations
- Geometry of Linear Algebra
- Rec 1 | MIT 18.085 Computational Science and Engineering I, Fall 2008
- An Overview of Key Ideas
- 2. Elimination with Matrices.
- Elimination with Matrices
- 3. Multiplication and Inverse Matrices
- Inverse Matrices
- 4. Factorization into A = LU
- LU Decomposition
- 5. Transposes, Permutations, Spaces R^n
- Subspaces of Three Dimensional Space
- 6. Column Space and Nullspace
- Vector Subspaces
- 7. Solving Ax = 0: Pivot Variables, Special Solutions
- Solving Ax=0
- 8. Solving Ax = b: Row Reduced Form R
- Solving Ax=b
- 9. Independence, Basis, and Dimension
- Basis and Dimension
- 10. The Four Fundamental Subspaces
- Computing the Four Fundamental Subspaces
- 11. Matrix Spaces; Rank 1; Small World Graphs
- Matrix Spaces
- 12. Graphs, Networks, Incidence Matrices
- Graphs and Networks
- 13. Quiz 1 Review
- Exam #1 Problem Solving
- 14. Orthogonal Vectors and Subspaces
- Orthogonal Vectors and Subspaces
- 15. Projections onto Subspaces
- Projection into Subspaces
- 16. Projection Matrices and Least Squares
- Least Squares Approximation
- 17. Orthogonal Matrices and Gram-Schmidt
- Gram-Schmidt Orthogonalization
- 18. Properties of Determinants
- Properties of Determinants
- 19. Determinant Formulas and Cofactors
- Determinants
- 20. Cramer's Rule, Inverse Matrix, and Volume
- Determinants and Volume
- 21. Eigenvalues and Eigenvectors
- Eigenvalues and Eigenvectors
- 22. Diagonalization and Powers of A
- Powers of a Matrix
- 23. Differential Equations and exp(At)
- Differential Equations and exp (At)
- 24. Markov Matrices; Fourier Series
- Markov Matrices
- 24b. Quiz 2 Review
- Exam #2 Problem Solving
- 25. Symmetric Matrices and Positive Definiteness
- Symmetric Matrices and Positive Definiteness
- 26. Complex Matrices; Fast Fourier Transform
- Complex Matrices
- 27. Positive Definite Matrices and Minima
- Positive Definite Matrices and Minima
- 28. Similar Matrices and Jordan Form
- Similar Matrices
- 29. Singular Value Decomposition
- Computing the Singular Value Decomposition
- 30. Linear Transformations and Their Matrices
- Linear Transformations
- 31. Change of Basis; Image Compression
- Change of Basis
- 33. Left and Right Inverses; Pseudoinverse
- Pseudoinverses
- 32. Quiz 3 Review
- Exam #3 Problem Solving
- 34. Final Course Review
- Final Exam Problem Solving