Vectors and Spaces
- Vectors
- Linear combinations and Spans
- Linear Dependence and Independence
- Subspaces and the basis for a subspace
- Vector dot and cross products
- Matrices for solving systems by elimination
- Null space and column space
Matrix transformations
- Functions and linear transformations
- Linear transformation examples
- Transformations and matrix multiplication
- Inverse functions and transformations
- Finding inverses and determinants
- More determinant depth
- Transpose of a matrix
Alternate Coordinate Systems (Bases)
- Orthogonal complements
- Orthogonal Projections
- Change of basis
- Orthonormal bases and the Gram-Schmidt process
- Eigen-everything
