1. MAT 4725 Numerical Analysis Section 7.1 Part I Norms of Vectors and Matrices http://myhome.spu.edu/lauw

2. Chapter 7 Iterative Techniques in Matrix Algebra Section 2.2 Fixed-Point Iteration

3. Chapter 7 Iterative Techniques in Matrix Algebra Section 7.3 Iterative Techniques

4. Chapter 7 Iterative Techniques in Matrix Algebra Section 7.3 Iterative Techniques

5. Chapter 7 Iterative Techniques in Matrix Algebra Section 7.3 Iterative Techniques

6. Chapter 7 Iterative Techniques in Matrix Algebra Section 7.3 Iterative Techniques We need a way to measure the distance between two vectors

7. 7.1 Norms of Vectors and Matrices Norms on real vector space (Part I) Norms on Matrices (Part II)

8. n Dimensional Real Vector Space Linear Algebra, Mult. Variables Calculus Applied Analysis

9. Definition 7.1

10. l 2 Norm (Euclidean Norm) Usual distance function on

11. l 2 Norm (Euclidean Norm) Usual distance function on Geometric Interpretations of

12. l  Norm Geometric Interpretations of

13. Example 1

14. Theorem 7.3 (Cauchy-Schwarz Inequality)

15. l 2 Norm is a vector norm Proof:

16. Definition 7.4

17. Definition 7.5

18. Theorem 7.6+7.7

19. Example 2

20. Classwork

21. Homework Download HW. Read 7.1 (skip all the proofs)