## MATH 340L. Matrices and Matrix Calculations-CS.

Unique #54310, Fall 2017

### Instructor

Prof. Todd Arbogast
E-Mail: arbogast@ices.utexas.edu
Office: RLM 11.162, Phone: 512-471-0166
Office hours: M 1:00-1:50 p.m. and W 12:30-2:30 p.m.

### Teaching Assistant

Hung-Ming Hsu
E-mail: hungming@utexas.edu
Office hours: TuTh 2:30-3:30 p.m. and F 2:00-4:00 p.m. in RLM 9.142

### Prerequisite

Mathematics 408C, 408K, or 408N with a grade of at least C-. Restricted to computer science majors. Mathematics 340L and 341 may not both be counted.

### Meeting

MWF 9-10:00 a.m. in RLM. in RLM 5.104. Attendance is required at all class meetings.

### Textbook

Gilbert Strang, Introduction to Linear Algebra, Fifth Edition, Wellesley-Cambridge Press, 2016, ISBN: 978-09802327-7-6, http://math.mit.edu/~gs/linearalgebra (Required).

### Class Web Site

We use the University's Canvas web site. Please check that your scores are recorded correctly in Canvas. You can access Canvas from my.utexas.edu.

### Course Outline

The numbers refer to Strang's textbook.

1. Introduction to Vectors (3 lectures)
1.1. Vectors and Linear Combinations
1.2. Lengths and Dot Products
1.3. Matrices

2. Solving Linear Equations (7 lectures)
2.1. Vectors and Linear Equations
2.2. The Idea of Elimination
2.3. Elimination Using Matrices
2.4. Rules for Matrix Operations
2.5. Inverse Matrices
2.6. Elimination = Factorization: A = LU
2.7. Transposes and Permutations

3. Vector Spaces and Subspaces (6 lectures)
3.1. Spaces of Vectors
3.2. The Nullspace of A: Solving Ax = 0 and Rx = 0
3.3. The Complete Solution to Ax = b
3.4. Independence, Basis and Dimension
3.5. Dimensions of the Four Subspaces

4. Orthogonality (5 lectures)
4.1. Orthogonality of the Four Subspaces
4.2. Projections
4.3. Least Squares Approximations
--- Alternate norms
4.4. Orthogonal Bases and Gram-Schmidt

5. Determinants (2 lectures)
5.1. The Properties of Determinants
5.2. Permutations and Cofactors
5.3. Cramer's Rule, Inverses, and Volumes

6. Eigenvalues and Eigenvectors (7 lectures)
6.1. Introduction to Eigenvalues
6.2. Diagonalizing a Matrix
10.3. Markov Matrices, Population, and Economics (from Chapter 10)
6.3. Systems of Differential Equations
6.4. Symmetric Matrices
6.5. Positive Definite Matrices

7. The Singular Value Decomposition (SVD) (4 lectures)
7.1 Image Processing by Linear Algebra
7.2 Bases and Matrices in the SVD
7.3 Principal Component Analysis (PCA by the SVD)
7.4 The Geometry of the SVD

8. Linear Transformations (3 lectures)
8.1. The Idea of a Linear Transformation
8.2. The Matrix of a Linear Transformation
8.3. The Search for a Good Basis

10. Applications (2 lectures, as time permits)
10.1 Graphs and Networks
10.6. Computer Graphics

### Computer Accounts

A computer account on the Mathematics Department network can be obtained in the Undergraduate Computer Lab, RLM 7.122.

### Homework and Quizzes

Homework and quizzes will be assigned regularly, with only a portion fully graded. Quizzes must be completed solely by the individual. For the homework, however, it is acceptable for groups of students to help each other; however, each student must write up his or her own work. Late homework will not be accepted for credit (unless there is a valid health issue), and homework must be turned in during class. The textbook web site has answers to the exercises.

### Exams

Three in-class exams will be given on Friday, Sept. 29, Oct. 27, and Nov. 17. A comprehensive final exam will be given Wednesday, Dec. 20, 9-12:00 noon.

Grades on the three midterm exams will be scaled to count 20 points each. For the homework and quizzes, the lowest score will be dropped, and the result will count as 20 points. The final exam will count 40 points. The final grade on the letter plus/minus scale will be determined out of 100 points by dropping the lowest midterm test grade, or by weighting the final test grade by 1/2 (i.e., count it as 20 points). The homework score will count in the final grade.

### Student Honor Code

"As a student of The University of Texas at Austin, I shall abide by the core values of the University and uphold academic integrity."

### Code of Conduct

The core values of The University of Texas at Austin are learning, discovery, freedom, leadership, individual opportunity, and responsibility. Each member of the university is expected to uphold these values through integrity, honesty, trust, fairness, and respect toward peers and community.

### Students with Disabilities

The University provides upon request appropriate academic accommodations for qualified students with disabilities. Contact the Office of the Dean of Students at 471-6259, 471-4641 TTY, and notify your instructor early in the semester.