In this chapter, we will learn about:
- Fields
- Vector spaces
- Examples
- Comments
- Linear dependence
- Linear combinations
- Bases
- Dimension
- Isomorphism
- Subspaces
- Calculus of subspaces
- Dimension of a subspace
- Dual spaces
- Brackets
- Dual bases
- Reflexivity
- Annihilators
- Direct sums
- Dimension of a direct sum
- Dual of a direct sum
- Quotient spaces
- Dimension of a quotient space
- Bilinear forms
- Tensor products
- Product bases
- Permutations
- Cycles
- Parity
- Multilinear forms
- Alternating forms
- Alternating forms of maximal degree
