Linear algebra
Vector spaces
- Introduction: Vector space
- Vector space
- Vector space: properties
- Proofs for vector spaces
- Field as a vector space
- Coordinate spaces
- Sequence spaces
- Function spaces
- Subspace
- Union and intersection of vector spaces
- Sum of subspaces
- Inner direct sum
- Complements of vector spaces
- Cosets of a subspace
- Quotient space
Linear combinations, generators and bases
Linear maps
- Linear map
- Properties of linear maps
- Linear continuation
- Proofs for linear maps
- Monomorphisms
- Epimorphisms
- Isomorphisms
- Endomorphism and Automorphism
- Image of a linear map
- Kernel of a linear map
- Vector space of a linear map
- Dual space
- Exercises