EE263: Matrix Methods: Singular Value Decomposition

Lecture slides

This list of slides will be added to during the quarter.

1. Overview

2. Linear functions

3. Engineering examples

4. Interpretations of linear equations

5. Linear algebra review

6. Range and null space

7. Rank

8. Orthogonality

9. QR factorization

10. Least-squares

11. Projectors

12. Example: Least-squares filtering

13. Example: Least-squares navigation

14. Multi-objective least-squares

15. Least-norm solutions of underdetermined equations

16. Recursive estimation

17. Least-squares fitting

18. LS via QR factorization

19. Gauss-Newton method

20. Eigenvectors and diagonalization

21. Symmetric matrices

22. Ellipsoids

23. Matrix norm

24. SVD and applications

25. Matrix facts

26. Gaussians

27. Conditional Gaussians

28. MMSE estimation

29. The linear model

30. Spectral graph embedding

Material from EE263 in 2024 that is now in EE363:

The slides below are on linear dynamical systems. These are from the old EE263, and will not be covered in Fall 2025. This material will be covered in EE363 in Spring.

1. Autonomous linear dynamical systems

2. Solution via matrix exponential

3. Dynamic interpretation of eigenvectors

4. Jordan canonical form

5. Linear dynamical systems with inputs and outputs

6. Controllability and state transfer

7. Observability and state estimation

8. Example: Input design

9. Example: Estimation and filtering

10. Example: Least-squares filtering revisited