Linear Algebra

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.