Linear Algebra (MIT 18.06)

Intermediate Mathematics by MIT OpenCourseWare. 36 lectures, 28.7 hours. Covers: matrices vectors eigenvalues eigenvectors determinants vector spaces null space rank svd least squares orthogonal projections.

Lectures

1. 1. The Geometry of Linear Equations · 40 min
2. Rec 1 | MIT 18.085 Computational Science and Engineering I, Fall 2008 · 50 min
3. 2. Elimination with Matrices. · 48 min
4. 3. Multiplication and Inverse Matrices · 47 min
5. 4. Factorization into A = LU · 48 min
6. 5. Transposes, Permutations, Spaces R^n · 48 min
7. 6. Column Space and Nullspace · 46 min
8. 7. Solving Ax = 0: Pivot Variables, Special Solutions · 43 min
9. 8. Solving Ax = b: Row Reduced Form R · 47 min
10. 9. Independence, Basis, and Dimension · 50 min
11. 10. The Four Fundamental Subspaces · 49 min
12. 11. Matrix Spaces; Rank 1; Small World Graphs · 46 min
13. 12. Graphs, Networks, Incidence Matrices · 48 min
14. 13. Quiz 1 Review · 48 min
15. 14. Orthogonal Vectors and Subspaces · 50 min
16. 15. Projections onto Subspaces · 49 min
17. 16. Projection Matrices and Least Squares · 48 min
18. Lec 17 | MIT 18.06 Linear Algebra, Spring 2005 · 49 min
19. 18. Properties of Determinants · 49 min
20. 19. Determinant Formulas and Cofactors · 53 min
21. 20. Cramer's Rule, Inverse Matrix, and Volume · 51 min
22. Lec 21 | MIT 18.06 Linear Algebra, Spring 2005 · 51 min
23. 22. Diagonalization and Powers of A · 52 min
24. 23. Differential Equations and exp(At) · 51 min
25. Lec 24 | MIT 18.06 Linear Algebra, Spring 2005 · 51 min
26. Lec 24b | MIT 18.06 Linear Algebra, Spring 2005 · 48 min
27. Lec 25 | MIT 18.06 Linear Algebra, Spring 2005 · 44 min
28. 26. Complex Matrices; Fast Fourier Transform · 48 min
29. 27. Positive Definite Matrices and Minima · 51 min
30. Lec 28 | MIT 18.06 Linear Algebra, Spring 2005 · 46 min
31. Lec 29 | MIT 18.06 Linear Algebra, Spring 2005 · 42 min
32. 30. Linear Transformations and Their Matrices · 49 min
33. Lec 31 | MIT 18.06 Linear Algebra, Spring 2005 · 50 min
34. 32. Quiz 3 Review · 47 min
35. 33. Left and Right Inverses; Pseudoinverse · 42 min
36. 34. Final Course Review · 43 min

Quick explainers

• Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra · 17 min
• What is an Eigenvector? · 4 min
• Finding Eigenvalues and Eigenvectors · 17 min
• Eigen values and Eigen vectors in 3 mins | Explained with an interesting analogy · 3 min
• The applications of eigenvectors and eigenvalues | That thing you heard in Endgame has other uses · 24 min
• No One Taught Eigenvalues & EigenVectors Like This · 9 min
• Eigenvalues & Eigenvectors — Finally Explained Visually! · 13 min
• You've Never Seen Eigenvectors Explained Like This · 14 min
• Eigenvectors and eigenvalues - simply explained · 12 min
• Introduction to eigenvalues and eigenvectors | Linear Algebra | Khan Academy · 8 min

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