Linear Algebra

1

An Interview with Gilbert Strang on Teaching Linear Algebra

2

1. The Geometry of Linear Equations

3

2. Elimination with Matrices.

4

3. Multiplication and Inverse Matrices

5

4. Factorization into A = LU

6

5. Transposes, Permutations, Spaces R^n

7

6. Column Space and Nullspace

8

7. Solving Ax = 0: Pivot Variables, Special Solutions

9

8. Solving Ax = b: Row Reduced Form R

10

9. Independence, Basis, and Dimension

11

10. The Four Fundamental Subspaces

12

11. Matrix Spaces; Rank 1; Small World Graphs

13

12. Graphs, Networks, Incidence Matrices

14

13. Quiz 1 Review

15

14. Orthogonal Vectors and Subspaces

16

15. Projections onto Subspaces

17

16. Projection Matrices and Least Squares

18

17. Orthogonal Matrices and Gram-Schmidt

19

18. Properties of Determinants

20

19. Determinant Formulas and Cofactors

21

20. Cramer's Rule, Inverse Matrix, and Volume

22

21. Eigenvalues and Eigenvectors

23

22. Diagonalization and Powers of A

24

23. Differential Equations and exp(At)

25

24. Markov Matrices; Fourier Series

26

24b. Quiz 2 Review

27

25. Symmetric Matrices and Positive Definiteness

28

26. Complex Matrices; Fast Fourier Transform

29

27. Positive Definite Matrices and Minima

30

28. Similar Matrices and Jordan Form

31

29. Singular Value Decomposition

32

30. Linear Transformations and Their Matrices

33

31. Change of Basis; Image Compression

34

32. Quiz 3 Review

35

33. Left and Right Inverses; Pseudoinverse

36

34. Final Course Review