1. Linear Equations, Back Substitution and Elementary Operations
    Reduction and Echelon Forms

  2. Vectors and Linear Combinations
    Matrix Equations
    Linear Independence

  3. Introductory Matrix Operations
    Matrix Multiplication
    Matrix Transforms
    Matrix Inverses

  4. Determinants: Definitions
    Calculating Determinants

  5. Subspaces and Closure
    Bases and Dimension

  6. The Three Matrix Spaces
    Coordinate Systems

  7. Vector Spaces
    Linear Transforms

  8. Eigenvalues
    Properties of Eigenvalues and Eigenvectors
    Similarity and Diagonalization

  9. The Dot Product and Orthogonal Vectors
    Orthogonal Complements and Orthonormal Matrices
    Iterative Orthogonalization