Lectures (Video)
- 1. The Geometry of Linear Equations
- 2. Elimination with Matrices
- 3. Multiplication and Inverse Matrices
- 4. Factorization into A = LU
- 5. Transposes, Permutations, Spaces R^n
- 6. Column Space and Nullspace
- 7. Solving Ax = 0: Pivot Variables, Special Solutions
- 8. Solving Ax = b: Row Reduced Form R
- 9. Independence, Basis, and Dimension
- 10. The Four Fundamental Subspaces
- 11. Matrix Spaces; Rank 1; Small World Graphs
- 12. Graphs, Networks, Incidence Matrices
- 13. Review
- 14. Orthogonal Vectors and Subspaces
- 15. Projections onto Subspaces
- 16. Projection Matrices and Least Squares
- 17. Orthogonal Matrices and Gram-Schmidt
- 18. Properties of Determinants
- 19. Determinant Formulas and Cofactors
- 20. Cramer's Rule, Inverse Matrix, and Volume
- 21. Eigenvalues and Eigenvectors
- 22. Diagonalization and Powers of A
- 23. Differential Equations and exp(At)
- 24. Markov Matrices; Fourier Series
- 25. Symmetric Matrices and Positive Definiteness
- 26. Complex Matrices; Fast Fourier Transform
- 27. Positive Definite Matrices and Minima
- 28. Similar Matrices and Jordan Form
- 29. Singular Value Decomposition
- 30. Linear Transformations and Their Matrices
- 31. Change of Basis; Image Compression
- 32. Review
- 33. Left and Right Inverses; Pseudoinverse
- 34. Final Review
Linear Algebra
Course Summary
This course is based on 18.06 Linear Algebra, Spring 2005 made available by Massachusetts Institute of Technology: MIT OpenCourseWare under the Creative Commons BY-NC-SA license.
This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. The lectures were conducted by Prof. Gilbert Strang at MIT in Spring 2005. Prof. Gilbert Strang is the author of the textbook Introduction to Linear Algebra used in the course.
Reading Material
1. Textbook (MIT 18.06): Introduction to Linear Algebra. 3rd ed.Strang, Gilbert. Introduction to Linear Algebra. 3rd ed. Wellesley, MA: Wellesley-Cambridge Press, March 2003. ISBN: 0961408898.
(Click the button below to see a preview of the book)
Course Material
1. Assignments (MIT 18.06 updated Spring 2010)Problem set 1 (pdf)
Problem set 2 (pdf)
Problem set 3 (pdf)
Problem set 4 (pdf)
Problem set 5 (pdf)
Problem set 6 (pdf)
Problem set 7 (pdf)
Problem set 8 (pdf)
Problem set 9 (pdf)
Problem set 10 (pdf)
2. Exams questions (MIT 18.06 updated Spring 2010)
| Exam 1 (pdf) | Solution 1 (pdf) |
| Exam 2 (pdf) | Solution 2 (pdf) |
| Exam 3 (pdf) | Solution 3 (pdf) |
| Final exam (pdf) | Solution Final (pdf) |
3. Eigenvalue Demonstrations
These are flash animations which were developed by Jean-Michel Claus (with voiceover by Gilbert Strang).
4. Mini-lectures on Eigenvalues
The mini-lectures are to help to explain some key Eigenvalue concepts.
5. Past exam questions (MIT 18.06)
Exam questions from past exams for review.
Other Resources
Not available.Software
1. Java applets for demonstrating linear algebra conceptsJava applets for demonstrating concepts in the course developed by Pavel Grinfeld.
- Eigenvalues
- SVD (Singular Value Decomposition)
- Gaussian Elimination
- Determinants
- Gram-Schmidt = Orthogonalization
- Inner Product of Functions
- Sum of Fourier Series
- Sum of Trigonometric Series
- Gibbs Phenomenon
- Aliasing
- Column Spaces
- Least Squares
- Power Method
