Vector Spaces
A 18-module path through vector spaces, in study order from foundations to the frontier.
Modules
- Systems of Linear Equations
- Gaussian Elimination and Row Reduction
- Fields
- Vector Spaces: Definition and Axioms
- Examples of Vector Spaces
- Subspaces
- Span and Linear Combinations
- Linear Independence
- Bases
- The Steinitz Exchange Lemma
- Dimension
- Coordinates Relative to a Basis
- Sums of Subspaces
- Direct Sums of Subspaces
- Dimension Formulas for Subspaces
- Quotient Spaces
- Dimension of Quotient Spaces
- Infinite-Dimensional Spaces