• Definition
• Examples -- F, Fⁿ, F[x], F[x,y], {f(x,y) | deg f=n}
• Linear independence
• Spanning
• Bases
• Dimension
• Subspaces
• Sums of subspcaes
• Direct sums
• Quotient spaces

1. Definition
2. Kernel and image
3. Isomorphism
4. Eigenspaces, eigenvectors, and eigenvalues
5. Hom(V,W) is a vector space
6. V^*=Hom(V,F)
7. V^* is isomorphic to V if and only if V is finite dimensional.
8. End(V)
9. GL(V)
10. Exact sequences

1. Sums, direct sums, and tensor products
2. Bilinear forms
   1. Symmetric and skew-symmetric forms
   2. Radical, nondegenerate bilinear forms
   3. Relation with linear functionals

1. of a linear transformation
2. of an endomorphism
3. of a bilinear form

1. Equivalence
2. Similarity
3. Contragradience

Toto, are we still in Kansas?