Starting a new Lecture Notes Series on MIT 18.06 Linear Algebra, Spring 2005
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MIT 18.06 Linear Algebra, Spring 2005 By Lecture Notes together!
Lecture 2: 1. The Geometry of Linear Equations
Lecture 3: 2. Elimination with Matrices.
Lecture 4: 3. Multiplication and Inverse Matrices
Lecture 5: 4. Factorization into A = LU
Lecture 6: 5. Transposes, Permutations, Spaces R^n
Lecture 7: 6. Column Space and Nullspace
Lecture 9: 8. Solving Ax = b: Row Reduced Form R
Lecture 10: 9. Independence, Basis, and Dimension
Lecture 11: 10. The Four Fundamental Subspaces
Lecture 12: 11. Matrix Spaces; Rank 1; Small World Graphs
Lecture 13: 12. Graphs, Networks, Incidence Matrices
Lecture 14: 13. Quiz 1 Review
Lecture 15: 14. Orthogonal Vectors and Subspaces
Lecture 16: 15. Projections onto Subspaces
Lecture 17: 16. Projection Matrices and Least Squares
Lecture 18: 17. Orthogonal Matrices and Gram-Schmidt
Lecture 19: 18. Properties of Determinants
Lecture 20: 19. Determinant Formulas and Cofactors
Lecture 21: 20. Cramer's Rule, Inverse Matrix, and Volume
Lecture 22: 21. Eigenvalues and Eigenvectors
Lecture 23: 22. Diagonalization and Powers of A
Lecture 24: 23. Differential Equations and exp(At)
Lecture 25: 24. Markov Matrices; Fourier Series
Lecture 26: 24b. Quiz 2 Review
Lecture 27: 25. Symmetric Matrices and Positive Definiteness
Lecture 28: 26. Complex Matrices; Fast Fourier Transform
Lecture 29: 27. Positive Definite Matrices and Minima
Lecture 30: 28. Similar Matrices and Jordan Form
Lecture 31: 29. Singular Value Decomposition
Lecture 32: 30. Linear Transformations and Their Matrices
Lecture 33: 31. Change of Basis; Image Compression
Lecture 34: 32. Quiz 3 Review
Lecture 35: 33. Left and Right Inverses; Pseudoinverse
Lecture 36: 34. Final Course Review