1. Linear Algebra Jean Walrand EECS – U.C. Berkeley

2. Outline Motivation Notation Key Results  Inverse  Range, Null Space  Factoring Hermitian Matrix  Singular Value Decomposition  Projection Notes

3. Motivation(1) Best approximation to x of the form a 1 v 1 + a 2 v 2 Filtering, estimation … = Projections

4. Motivation(2) Markov Chain

5. Notation

6. Key Results 1. Inverse

7. Key Results 2. Range, Null Space

8. Key Results 3. ONB of Eigenvectors for Hermitian Matrix

9. Key Results 4. SVD of general matrix

10. Key Results 5. Projection

11. Key Results 5. Projection

12. Key Results 5. Projection

13. Notes References: Notes on class web page Discussion this week We assume that you are able to use the “key results” Test next week on your understanding of the key results