1. Vectora and Spaces:
Introduction to vectors, Real coordinate spaces, Multiplication, 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.
2. Matric 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.
3. Alternate coordinate systems:
Orthogonal complements, Orthogonal projections, Change of basis, Orthonormal bases and the Gram-Schmidt process, Eigen-everything.