| 1 |
1.1 Systems of Linear Equations, 1.2 Row Reduction and Echelon Forms, 1.3 Vector Equations |
| 2 |
1.4 The Matrix Equation Ax=b, 1.5 Solution Sets of Linear Systems |
| 3 |
1.7 Linear Independence, 1.8 Introduction to Linear Transformations |
| 4 |
1.9 The Matrix of a Linear Transformation, 2.1 Matrix Operations, 2.2 The Inverse of a Matrix |
| 5 |
2.3 Characterizations of Invertible Matrices, 3.1 Introduction to Determinants |
| 6 |
3.2 Properties of Determinants, 4.1 Vector Spaces and Subspaces (introduce complex vector spaces and examples too) |
| 7 |
4.2 Null Spaces, Column Spaces, and Linear Transformations, 4.3 Linearly Independent Sets; Bases |
| 8 |
4.4 Coordinate Systems, 4.5 The Dimension of a Vector Space, 4.6 Change of Basis |
| 9 |
5.1 Eigenvectors and Eigenvalues, 5.2 The Characteristic Equation, 5.5 Complex Eigenvalues |
| 10 |
5.3 Diagonalization, 6.1 Inner Product (including Hermitian), Length, and Orthogonality, 6.2 Orthogonal Sets |
| 11 |
6.3 Orthogonal Projections, 6.4 The Gram-Schmidt Process |
| 12 |
6.5 Least-Squares Problems, 7.1 Diagonalization of Symmetric Matrices |
| 13 |
7.2 Quadratic Forms, 7.4 The Singular Value Decomposition |