| Lectures | Sections in Text | Brief Description |
|---|---|---|
| 3/27 | 1.1 | Systems of Linear Equations |
| 3/29 | 1.2 | Row Reduction and Echelon Forms |
| 3/31 | 1.3, 1.4 | Vector Equations; Matrix Equations |
| 4/3 | 1.4, 1.5 | Matrix Equations; Solutions Sets of Linear Equations |
| 4/5 | 1.7 | Linear Independence |
| 4/7 | 4.1, 4.2 | Vector spaces, linear transformation, null space, column space |
| 4/10 | 4.2, 1.9 | Reading injectivity and surjectivity of $T: \mathbb R^n \to \mathbb R^m$ from the representing matrix. |
| 4/12 | 1.9, 2.1 | Matrix Operations |
| 4/14 | 2.2 | Inverse of a Matrix |
| 4/17 | 2.3 | Invertible Matrix Theorem |
| 4/19 | 4.3 | Linear independent sets; bases |
| 4/20 | First Midterm | 4:30-6:30pm |
| 4/21 | 2.9 | Dimension and rank |
| 4/24 | 4.4/4.7/5.4 (variant) | Coordinates, matrix of a transformation, change of basis |
| 4/26 | 4.7, 3.1 | Determinants and Properties |
| 4/28 | 3.2 | Properties of Determinants |
| 5/1 | 5.1, 5.2 | Eigenvalues and Characteritic Equation |
| 5/3 | 5.2, 5.3 | Characteristic Equation, Diagonalization |
| 5/5 | 5.3, 5.4 | Diagonalization and linear transformations |
| 5/8 | 4.9,5.8 | (optional) Intro to Markov Chains, Iteration Method for Eigenvalues |
| 5/10 | 6.1-6.2 | Orthogonality |
| 5/11 | Second Midterm | 4:30-6:30pm |
| 5/12 | 6.3 | Projections |
| 5/15 | 6.4 | Gram-Schmidt Process |
| 5/17 | 7.1 | Diagonalization of Symmetric Matrices |
| 5/19 | 7.4 | Singular Value Decomposition |
| 5/22 | 7.4 | Singular Value Decomposition |
| 5/24 | 7.4, 7.5 | Other applications, e.g., Principal
Component Analysis, SVD and image processing, Facial Recognition, etc. |
| 5/26 | Wrap it up | |
| 5/29 | Memorial Day Holiday | No classes |
| 6/1 | Final Exam | 11:30 am - 2:30 pm |