Linear Algebra

Solving systems of linear equations (using Gaussian elimination)

Vectors in R^n

Linear dependence/independence

Matrix algebra (sum, product, inverse)

LU decomposition of a matrix

Lineare transformations

Subspaces in R^n (basis, dimension); column space and null space

Determinants

Eigenvalues and eigenvectors

Diagonalization

Inner products and orthogonal sets

Orthogonal projections

Method of least squares and linear models

Symmetric matrices