Content
1. An overview of key ideas .
2. Elimination with Matrices
3. Multiplication and Inverse Matrices .
4. Factorization into A = LU
5. Transposes, Permutations, Vector Spaces .
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. Exam 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. .
21. Eigenvalues and eigenvectors .
22. Diagonalization and powers of A .
23. Differential equations and eAt .
24. Markov matrices; Fourier series ..
25. Exam 2 Review
26.
27. Complex matrices; fast Fourier transform
28. Positive definite matrices and minima .
29. Similar matrices and Jordan form
30. Singular value decomposition ..
31. Linear transformations and their matrices
32. Change of basis; image compression ...
33. Exam 3 review ..
34. Left and right inverses; pseudoinverse .
35. Final course review
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