1. CS232

2. Schedule 1. Introduction 2. Points vs vector (distance, balls, sphere)
Chapter 1
3. Divide and Conquer: Algorithms for Near Neighbor Problem
Handout (section)

3. 4. Hyperplanes Chapter 2 Ray intersections Lines By linear equations
By two points
When does a line passing the origin
Intersection of two lines
Matrix and algebraic approach (two variables and two equations)

4. 3D Ray and mirrors Planes in three dimensions By linear equations
By three points
When does a plane passing the origin

5. Hyperplanes Hypereplanes in n-dimensions Intersection of three planes
Matrix and algebraic approach (three variables and equations)
Hypereplanes in n-dimensions
By linear equations
By n points
When does a hyperplane passing through the origin
Intersection of n hyperplanes in n dimensions

6. Matrix Form What is a matrix? Matrix vector multiplication
(inner product after all)
Matrix form of intersection of n hyperplanes --- system of linear equations?

7. Column Picture: combination of vectors
Find proper linear combinations of vectors
Visualize hyperplane is hard, so you might eventually like the column pictures.

8. Repeated the questions
Row pictures: n hyperplanes meets at a single points
Column pictures: combines n vectors to produce another vector

9. Gaussian Elimination Gaussian Elimination in 2 dimensions example
Pictures
Pivots
Multipliers
Upper triangular matrix
Back substitution

10. Two dimensions Unique solution No solution Infinitely many solutions
What if the pivot is 0!!!

11. 3D Gaussian Elimination in 3 dimensions
example
Pictures
Pivots
Multipliers
Upper triangular matrix
Back substitution
Can be extended to any dimensions

12. 5. Gaussian Elimination (General form)
Matrix Algebra
Matrix addition
Scalar times a matrix
Matrix multiplication
(dimensions have to agree)
Associative law
Non commutative law

13. Gaussian Elimination (General form)
Identity matrix
Elimination matrix

14. Permutation Matrix

15. Matrix algebra (General form)
All the laws (page 58 – 59)

16. Complexity of Matrix Multiplication
cube

17. Block Multiplication

18. Strassen’s Fast Matrix Mulplication
Divide and conquer

19. 6. Inverse Matrix 7 Quiz 1 8 LU factorization
Rest of chapter 2

20. 9. Two dimensional convex Hull
From the handout
Convex combination

21. 10. Algorithms for Null space
3.1 – 3.3

22. 11. Complete Linear Solver
3.4 – 3.6

23. 12. No class 13 Geometric Projection
4.1 – 4.2

24. 14. Midterm 15 Least Square Algorithm

25. 16. QR Decomposition

26. 17-18 no classes spring break

27. 19. Hubs and Authority Theory for Webs Hand out
Understanding webs
How Google works

28. 20. Simplex and its Volume
Chapter 5

29. 21. Determinants: Matrix Representation of volume

30. 22. Eivenvalue problem and Spectral Geometry

31. 23. Quiz 2

32. 24. Diagonalization

33. 25. Quadratic Shapes
Positive Definite matrices

34. 26. Dimensional Reduction
Singular value Decomposition

35. 27. Application: Computer Graphics

36. 28. Spherical Geometry Points on sphere Caps
Stereographic Transformation

37. 29. Geometric Transformation
Chapter 7

38. 30 Geometric Transformation

39. 31. Triangulations and Voronoi Diagram