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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
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