1.1   Introduction to linear systems
1.2   Matrices, vectors and Gauss-Jordan elimination
1.3   On the solutions of linear systems: matrix algebra

2.1   Introduction to linear transformations and their inverses
2.2   Linear transformations in geometry
2.3   The inverse of a linear transformation
2.4   Matrix products

3.1   Image and kernel of a linear transformation
3.2   Subspaces of R^n; bases and linear independence
3.3   The dimension of a subspace of R^n
3.4   Coordinates

4.1   Skip - Introduction to linear spaces
4.2   Skip - Libear transformations and isometries
4.3   Skip - The matrix of a linear transformation

5.1   Orthogonal projection and orthonormal bases
5.2   Gram-Schmidt process and QR factorization
5.3   Orthogonal transformations and orthogonal matrices
5.4   Least squares and data fitting
5.5   Skip - Inner product spaces

6.1   Introduction to determinants
6.2   Properties of the determinant
6.3   Geometrical interpretations of the determinant; Cramer's rule

7.1   Dynamical systems and eigenvectors: an introductory example
7.2   Finding the eigenvalues of a matrix
7.3   Finding the eigenvectors of a matrix
7.4   Diagonalization
7.5   Complex eigenvalues
7.6   Stability

8.1   Symmetric matrices
8.2   Quadratic forms
8.3   Singular values

9.1   Skip - An introduction to continuous dynamical systems
9.2   Skip - The complex case: Euler's formula
9.3   Skip - Linear differential operators and linear differential equations