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1. Vectors, what even are they?

2. Linear combinations, span, and basis vectors

3. Linear transformations and matrices

4. Matrix multiplication as composition

5. Three-dimensional linear transformations

6. The determinant

7. Inverse matrices, column space and null space

8. Nonsquare matrices as transformations between dimensions

9. Dot products and duality

10. Cross products

11. Cross products in the light of linear transformations

12. Cramer's rule, explained geometrically

13. Change of basis

14. Eigenvectors and eigenvalues

15. A quick trick for computing eigenvalues

16. Abstract vector spaces