$$

Reading materials

1. Learning resources from Linear Algebra I
2. Handout: matrix-tree theorem
3. Wrong way to find the determinant
4. Video: definition of the determinant
5. Definition of the determinant: Hefferon Four.I.1 ~ 2
6. Find the determinant
7. Video: elementary matrix
8. Write a matrix as the product of elementary matrices
9. Geometry of Determinants: Hefferon Four.II
10. Matrices with dependent rows
11. Distributive law
12. Permutation expansion: Hefferon Four.I.3
13. Laplace expansion: Hefferon Four.I.3
14. Matrix multiplication and transpose
15. Block matrix
16. Midterm 1: Questions to ponder
17. The Method of Least Squares
18. Image compression by singular value decomposition
19. Similarity: Hefferon Five.II
20. Observe a matrix from a different basis: LR of Math103A 31~35
21. Quadratic curve
22. Diagonalization
23. Find a good basis
24. Characteristic polynomial
25. Find the characteristic polynomial
26. Vieta's formula
27. Diagonalizable or not
28. Midterm 2: Questions to ponder
29. Projection
30. Least squares problem
31. Linear regression
32. Polynomial regression
33. Basic NumPy
34. Find an orthonormal basis of a subspace
35. Find an orthonormal basis composed of eigenvectors
36. Find the spectral decomposition
37. Rayleigh quotient of a diagonal matrix
38. Rayleigh quotient of a real symmetric matrix
39. Singular value decomposition
40. AB and BA have the same nonzero eigenvalues
41. Find the singular value decomposition
42. Final exam: Questions to ponder