Linear Algebra
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