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Massachusetts Institute of Technology via YouTube Video playlist
MIT 18.06 Linear Algebra, Spring 2005
Overview
Instructor: Prof. Gilbert Strang
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. *Please note that lecture 4 is unavailable in a higher quality format.
Find more lecture notes, study materials, and more courses at http://ocw.mit.edu.
Videos in this playlist 36
- An Interview with Gilbert Strang on Teaching Linear Algebra
- 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. Quiz 1 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
- 24b. Quiz 2 Review
- 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. Quiz 3 Review
- 33. Left and Right Inverses; Pseudoinverse
- 34. Final Course Review
Advantages and disadvantages
Advantages
- Free and complete: every lecture is in the playlist, in order.
- Watch at 1.5x, skip what you know, rewatch what you don't.
- Taught by Massachusetts Institute of Technology, one of the strongest names in its field.
- 3,365,342 views, so help and notes are easy to find.
- Completely free.
- Self-paced: start any time.
- A clear syllabus (36 videos) you can see before you start.
- Start watching right away, no sign-up.
Disadvantages
- No certificate, deadlines or graded work.
- Quality and depth vary: check that the playlist is finished before you start.
- No certificate.
- No graded assignments or feedback.
Some points apply to every course of this kind; see how we rank.
Free
- Free: Watch on YouTube, no account needed.
- Certificate: None. Code or take notes along to make it stick.
Massachusetts Institute of Technology is in Tier 1: world-leading universities and India's top institutes of our institution ranking (98/100). OpenCourseWare is the gold standard for free university material.
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