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

*Unique #54170, Fall 2016*

### Instructor

Prof. Todd Arbogast

E-Mail: arbogast@ices.utexas.edu

Office: RLM 11.162, Phone: 512-471-0166

Office hours: M 12:30-1:50 p.m. and Th 8:30-10:00 a.m.

### Teaching Assistant

Mr. Yibo Hu

E-mail: huyibodtc@gmail.com

Phone 608-698-4380

Office hours: MTu 10:00-10:45 a.m. (in STEM Learning Center, first
floor of PCL)
and WTh 7:00-8:00 p.m. (WEL 2.228)

### 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

9-10:00 a.m. in CPE 2.214.
Attendance is required at all class meetings.
### Textbook

Gilbert Strang, *Introduction to Linear Algebra,* Fourth Edition,
Wellesley-Cambridge Press, Wellesley, MA, 2009, ISBN 978-09802327-14.
(We use the 4th edition, but you might find the 5th edition's web site
useful: http://math.mit.edu/linearalgebra.)
### 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. We also have a piazza page for class discussion, if you wish to use it.
### 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 (8 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 (7 lectures)

3.1. Spaces of Vectors

3.2. The Nullspace of *A*: Solving *Ax = 0*

3.3. The Rank and the Row Reduced Form

3.4. The Complete Solution to *Ax = b*

3.5. Independence, Basis and Dimension

3.6. 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 (1 lecture)

5.1. The Properties of Determinants

6. Eigenvalues and Eigenvectors (8 lectures)

6.1. Introduction to Eigenvalues

6.2. Diagonalizing a Matrix

8.3. Markov Matrices, Population, and Economics (from Chapter 8)

6.3. Applications to Differential Equations

6.4. Symmetric Matrices

6.6. Similar Matrices

6.7. Singular Value Decomposition (SVD)

7. Linear Transformations (3 lectures)

7.1. The Idea of a Linear Transformation

7.2. The Matrix of a Linear Transformation

--- Examples on R^{n}: rotations, projections, shears, and reflections

7.3. Diagonalization and the Pseudoinverse

8.7. Computer Graphics (1 lecture, as time permits)

### Computer Accounts

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

Homework will be assigned weekly, with only a portion to be fully
graded. It is acceptable for groups of students to help each other
with the homework exercises; 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 has answers to selected exercises.
### Exams

Three in-class exams will be given on Friday, Sept. 23, Oct. 21, and
Nov. 18. A comprehensive final exam will be given Saturday, Dec. 10,
2-5:00 p.m. in CPE 2.214
### Final Grade

Grades on the three midterm exams will be scaled to count 20 points
each. For the homework, 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.
### Religious Holidays

Academic accommodation is made for major religious holidays upon
request.
### Emergency Classroom Evacuation

Occupants of University of Texas buildings are required to
evacuate when a fire alarm is activated. Alarm activation or announcement requires exiting and
assembling outside. Familiarize yourself with all exit doors of each classroom and building you may
occupy. Remember that the nearest exit door may not be the one you used when entering the building.
Do not re-enter a building unless given instructions by the Austin Fire Department, the University
Police Department, or the Fire Prevention Services office.
### Counseling and Mental Health Services

Available at the Counseling and Mental Health
Center, Student Services Building (SSB), 5th floor, M-F 8:00 a.m. to 5:00 p.m., phone 512-471-3515,
web site www.cmhc.utexas.edu.