| Lecture |
Section in Text
|
Brief Description
|
|---|
| Day 1 |
1.1
|
Systems of Linear Equations
|
| Day 2 |
1.2
|
Row Reduction and Echelon Forms
|
| Day 3 |
1.3 & 1.4
|
Vector Equations; Matrix Equations
|
| Day 4 |
1.4 -1.5
|
The Matrix Equation Ax=b and Solution Sets of Linear Equations
|
| Day 5 |
1.7
|
Linear Independence
|
| Day 6 |
4.1, 4.2
|
Vector spaces, linear transformation, null space, column space
|
| Day 7 |
4.2, 1.9
|
Definition of Linear Transformations, Kernel and Range and the
standard matrix
|
| Day 8 |
1.9, 2.1
|
Reading Injectivity and Surjectivity of T: Rn --> Rm from the matrix
and Matrix Operations
|
| Day 9 |
2.2
|
Inverse of a Matrix
|
| Day 10 |
2.3
|
Invertible Matrix Theorem
|
| Day 11 |
4.3 |
Linear independent sets; bases |
| |
Week 4 |
MIDTERM #1 |
| Day 12 |
2.9 |
Coordinates, Dimension and rank
|
| Day 13 |
4.4/5.4/4.7
|
Matrix of a transformation, Change of coordinates matrix
|
| Day 14 |
4.7
|
Change of coordinates matrix and composition of linear transformations
|
| Day 15 |
3.1, 3.2
|
Determinant and its Properties of Determinants
|
| Day 16 |
5.1, 5.2
|
Eigenvalues and Characteristic Equation
|
| Day 17 |
5.2, 5.3
|
Characteristic Equation, Diagonalization
|
| Day 18 |
5.3, 5.4
|
Diagonalization and linear transformations
|
| Day 19 |
6.1, 6.2
|
Inner products and Orthogonality
|
| Day 20 |
6.3
|
Projections
|
| |
Week 7 |
MIDTERM #2 |
| Day 21 |
6.4
|
Gram-Schmidt Process
|
| Day 22 |
7.1
|
Diagonalization of Symmetric Matrices
|
| Day 23 |
4.9, 5.8
|
Intro to Markov Chains, Iteration Method for Eigenvalues
|
| Day 24
|
4.9, 5.8
|
Application: Markov Chains & Google's page rank
|
| Day 25 |
7.4
|
Application: Singular Value decomposition (SVD)
|
| Day 26 |
7.5
|
Principal Component Analysis (PCA) & Eigenfaces
|
| Day 27 |
No section in book
|
Application -- JPEG compression algorithm.
|
| Day 28 |
No section in book
|
Review
|