Syllabus

The following is a tentative syllabus for the course. This page will be updated irregularly. On the other hand, the weekly syllabus contained in on Canvas will always be accurate.

Lecture Date Sections in Text Brief Description
1 9/12 1.1 Systems of linear equations
2 9/14 1.2 Row reduction and echelon forms
3 9/16 1.3, 1.4 Vector equations; Matrix equations
4 9/19 1.4, 1.5 The matrix equation Ax=b and solutions sets of linear equations
5 9/21 1.7 Linear independence
6 9/23 4.1, 4.2 Vector spaces, linear transformation, null space, column space
7 9/26 4.2, 1.9 Definition of linear transformations, kernel and range, the standard matrix
8 9/28 1.9, 2.1 Reading injectivity and surjectivity of T:Rn --> Rm from the matrix, and matrix operations
9 9/30 2.2 Inverse of a matrix
10 10/3 2.3 Invertible Matrix Theorem
11 10/5 4.3 Linearly independent sets; bases
10/6 Exam 1
12 10/7 2.9 Coordinates, dimension, and rank
13 10/10 4.4, 5.4, 4.7 Matrix of a transformation, change of coordinates matrix
14 10/12 4.7 Change of coordinates matrix and composition of linear transformations
15 10/14 3.1, 3.2 Determinants and properties of determinants
16 10/17 5.1, 5.2 Eigenvalues and the characteristic equation
17 10/19 5.2, 5.3 The characteristic equation, diagonalization
10/21 No class for Day of Caring
18 10/24 5.3, 5.4 Diagonalization and linear transformations
19 10/26 6.1, 6.2 Inner products and orthogonality
10/27 Exam 2
20 10/28 6.3 Projections
21 10/31 6.4 Gram-Schmidt process
22 11/2 7.1 Diagonalization of symmetric matrices
23 11/4 4.9, 5.8 Intro to Markov chains, iteration method for eigenvalues
24 11/7 4.9, 5.8 Application: Markov chains and Google's page rank
25 11/9 7.4 Application: Singular value decomposition (SVD)
26 11/11 7.5 Principal component analysis (PCA) and eigenfaces
27 11/14 Review for the final exam