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 - Lecture 16
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Lecture 16 - Projection Matrices and Least Squares
Prof. Gilbert Strang
18.06 Linear Algebra, Spring 2005 (Massachusetts Institute of Technology: MIT OpenCourseWare) http://ocw.mit.edu Date accessed: 2008-12-24 License: Creative Commons BY-NC-SA |
