

Introduction 
Gaussian elimination 
Homogeneous systems 
Matrices 
Matrix multiplication 
Block multiplication 
Inverse matrices 
Elementary matrices 
LU factorization 
Laplace expansion 
Properties of the determinant 
Determinants and matrix inverses 
Adjoints and Cramer's rule 
Complex numbers 
Eigenvalues and eigenvectors 
Diagonalization 
Dynamical systems 
Vectors 
Lines in space 
Dot product 
Projections 
Planes 
Cross product 
Triangles and parallelepipeds 
Least squares approximation 
Subspaces 
Spans 
Linear independence 
Rank 
Bases 
Similar matrices 
Eigenspaces 
Linear transformations 
Matrices of linear transformations 
Polynomials in vector spaces 
Properties of polynomials 
