| Lecture |
Date |
Section in Text
|
Brief Description
|
|---|
| Day 1 |
Mon. March 31
|
1.1
|
Systems of Linear Equations
|
| Day 2 |
Wed. April 2
|
1.2
|
Row Reduction and Echelon Forms
|
| Day 3 |
Fri. April 4
|
1.3 1.4
|
Vector Equations; Matrix Equations
|
| Day 4 |
Mon. April 7
|
1.4 -1.5
|
The Matrix Equation Ax=b and Solution Sets of Linear Equations
|
| Day 5 |
Wed. April 9
|
1.7
|
Linear Independence
|
| Day 6 |
Fri. April 11
|
4.1, 4.2
|
Vector spaces, linear transformation, null space, column space
|
| Day 7 |
Mon. April 14
|
4.2, 1.9
|
Definition of Linear Transformations, Kernel and Range and the
standard matrix
|
| Day 8 |
Wed. April 16
|
1.9, 2.1
|
Reading Injectivity and Surjectivity of T: Rn --> Rm from the matrix
and Matrix Operations
|
| Day 9 |
Fri. April 18
|
2.2
|
Inverse of a Matrix
|
| Day 10 |
Mon. April 21 |
2.3
|
Inverse Matrix Theorem
|
| Day 11 |
Wed. April 23 |
4.3 |
Linear independent sets; bases |
| |
Thrs. April 24 |
|
MIDTERM #1 |
| Day 12 |
Fri. April 25
|
2.9 |
Coordinates, Dimension and rank
|
| Day 13 |
Mon. April 28 |
4.4/5.4/4.7
|
Matrix of a transformation, Change of coordinates matrix
|
| Day 14 |
Wed. April 30 |
4.7
|
Change of coordinates matrix and composition of linear transformations
|
| Day 15 |
Fri. May 2 |
3.1, 3.2
|
Determinant and its Properties of Determinants
|
| Day 16 |
Mon. May 5 |
5.1, 5.2
|
Eigenvectors and Eigenspaces
|
| Day 17 |
Wed. May 7 |
5.2, 5.3
|
Eigenvalues and Characteristic Equation
|
| Day 18 |
Fri. May 9
|
5.3, 5.4
|
Diagonalization and linear transformations
|
| Day 19 |
Mon. May 12 |
6.1, 6.2
|
Inner products and Orthogonality
|
| Day 20 |
Wed. May 14 |
6.3
|
Projections
|
| |
Thrs. May 15 |
|
MIDTERM #2 |
| Day 21 |
Fri. May 16 |
6.4
|
Gram-Schmidt Process and Least Squares
|
| Day 22 |
Mon. May 19 |
7.1
|
Diagonalization of Symmetric Matrices
|
| Day 23 |
Wed. May 21
|
4.9, 5.8
|
Intro to Markov Chains, Iteration Method for Eigenvalues
|
| Day 24
|
Fri. May 23
|
4.9, 5.8
|
Application: Markov Chains & Google's page rank
|
| Day 25 |
Tues. May 27 (x-hour) |
7.4
|
Application: Singular Value decomposition (SVD)
|
| Day 26 |
Wed. May 28 |
7.4
|
Application of SVD to storing images
|
| Day 27 |
Fri. May 30 |
No section in book
|
Application -- JPEG compression algorithm
|
| Day 28 |
Mon. June 2 |
Section 7.5
|
Application: Principal Component Analysis (PCA) & Eigenfaces
|