**Notes, Quizzes, Solutions, Etc.** on DropBox (accessible by students only)

**Description**: Linear Algebra is the most important subject in mathematics in your undergraduate career. Until recently, that subject was Calculus but as computers replaced pen and paper the focus shifted to Linear Algebra since it emphasizes discrete rather than continuous methods. Linear Algebra is the glue that bonds together all branches of mathematics.

Linear algebra studies the common properties shared by all objects that can be added together and multiplied by a number. Such objects include geometric vectors, polynomials (and, more generally, functions), matrices, transformations and many others. Because Linear Algebra simultaneously studies diverse objects, the language of Linear Algebra is necessarily abstract. As you become more proficient in this language, you will develop the ability to make precise and disciplined arguments.

**Topics**:

1. My three favorite examples: vectors, polynomials, R^n

2. Addition and linear combinations

3. Decomposition with respect to a basis

4. Further examples of decomposition

5. Linear independence

6. Linear independence continued

7. Linear systems

8. The null space and the column space

9. The null space and the column space continued

10. More on the null space

11. Gaussian elimination

12. Matrix multiplication – Introduction

13. Matrix multiplication continued

14. Elementary matrices

15. The inverse

16. The LU decomposition

17. Linear transformations

18. Eigenvalues and eigenvectors

19. Matrix Representation of a linear transformation

20. Matrix eigenvalues and eigenvectors

21. Techniques for identifying eivanvalues and eigenvectos

22. The eigenvalue decomposition

23. The inner product

24. Matrix representation of an inner product