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. Matrix Products
2.4. The Inverse of a Linear Transformation
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. Introduction to Linear Spaces
4.2. Linear Transformations and Isomorphisms
4.3. The Matrix of a Linear Transformation
6.1. Introduction to Determinants
6.2. Properties of the Determinant
6.3. Geometrical Interpretations of the Determinant (skip 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
5.1. Orthogonal Projections 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