Lauren Patterson presentation on Matrix Groups and Symmetry for MAT 361 (Modern Algebra), Franklin College, Fall 2009.

1. Matrix Groups and Symmetry Lauren Patterson

2. Linear Algebra Results Linear Transformations Invertible Matrices Properties of determinants Properties of Euclidean inner products

3. Matrix Groups

4. The Orthogonal Group

5. Geometric Approach

6. Example

7. Determinant of Orthogonal Matrices The determinant of any orthogonal matrix is 1 or -1.

8. Theorem 10.2 Let A be an n x n matrix. The following statements are equivalent:

9. Symmetry