Topics
Foundations of linear algebra
- Vector space and subspace axioms
- Linear combinations and spanning
- Linear independence
- Bases and dimension
Theorems:
- (Theorem) The size of a linearly independent set is less than or equal to the size of its spanning set
- (Theorem) A subspace of a finite-dimensional vector space has dimension less than or equal to the latter’s
Foundations of linear maps
- Linear maps
- Image and kernel
- Compositions and invertible linear maps
- Different perspectives of matrices
- Composition and matrix multiplication
Theorems:
- (Theorem) Linear maps are determined by their values on a basis
- (Theorem) Rank-nullity
- (Theorem) Invertible matrix