Matrix Theory: We compute the exponential of a real 2x2 matrix A when the trace of A is zero. We use the Cayley-Hamilton Theorem to obtain explicit formulas based on the determinant of A.

1. Matrix Inverse over the Complex Numbers
2. Cramer's Rule over the Complex Numbers
3. Gaussian Elimination over Z/3
4. Matrix Inverse over Z/7
5. Cramer's Rule over Z/5
6. Example of Skew-Symmetric Matrix
7. Example of Simultaneous Diagonalization
8. Positive Semi-Definite Matrix 1: Square Root
9. Positive Semi-Definite Matrix 2: Spectral Theorem
10. Positive Semi-Definite Matrix 3: Factorization of Invertible Matrices
11. Cayley-Hamilton Theorem for 2x2 Matrices
12. Inverse of a Matrix Using the Cayley-Hamilton Theorem
13. Cayley-Hamilton Theorem: General Case
14. Cayley-Hamilton Theorem: Example 1
15. Cayley-Hamilton Theorem Example 2
16. Example of Invariant Subspace
17. Overview of Jordan Canonical Form
18. Example of Jordan Canonical Form: 2x2 Matrix
19. Example of Jordan Canonical Form: General Properties
20. Example of Jordan Canonical Form: Real 4x4 Matrix with Basis 1
21. Example of Jordan Canonical Form: Real 4x4 Matrix with Basis 2
22. Commutant of Complex Matrix
23. Example of Rational Canonical Form 1: Single Block
24. Example of Rational Canonical Form 2: Several Blocks
25. Example of Rational Canonical Form 3
26. Exponential of 2x2 Matrix 1: Complex Case
27. Exponential of 2x2 Matrix 2: Traceless Case
28. Example of Group Action
29. Example of Quaternions
30. The Fibonacci Numbers Using Linear Algebra (HD Version)
31. The Fibonacci Numbers Using Power Series
32. Example of Group Automorphism 1 (Requires Linear Algebra)
33. Example of Group Automorphism 2: G = Z/4 x Z/4 (Requires Linear Algebra)
34. Group Theory: The Simple Group of Order 168 - Part 1
35. Group Theory: The Simple Group of Order 168 - Part 2

This set contains linear algebra over fields other than R and topics concerning matrices, such as canonical forms and groups.