1. Linear Algebra (Aljabar Linier) Week 13 Universitas Multimedia Nusantara Serpong, Tangerang Dr. Ananda Kusuma e-mail: ananda_kusuma@yahoo.com

2. Agenda Review Distance and Approximation –Inner product spaces, norms and distance functions –Least Squares approximation Quiz

3. 1) Review

4. Inner Product Spaces Norms and Distance Functions

5. Length, Distance and Orthogonality Inner Product Space

6. a) Examples

7. Examples: a) Sum norm: b) Max norm: c) P-norm: d) 2-Norm or Euclidean norm: Normed Vector Space

8. Least Squares Approximation

9. Motivation: Curve of best fit

10. Best Approximation

11. -Minimizing total error -Example: n data points and a line -The error vector is where -We can construct a system of linear equation in matrix form, where -The error vector Least Square for Curve Fitting

12. Least Square Theorem

13. Find the parabola that gives the best least-squares approximation to the points (-1,1), (0,-1),(1,0), and (2,2) Example

14. The End Thank you for your attention!