M 340L. Matrices and Matrix Calculations–CS.

Unique #52970, Fall 2019


Prof. Todd Arbogast
Office: RLM 11.162, Phone: 512-471-0166
E-Mail: arbogast@ices.utexas.edu
Office hours: WTh 8:40-10:00.


M 408C, 408K, or 408N with a grade of at least C-. Restricted to computer science majors. Only one of the following may count: M 340L, M 341, SDS 329C, or SSC 329C.


MWF 11:00 a.m.-12:00 noon in GSB 2.126. Attendance isrequired at all class meetings.


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

Web Pages:

We use the University's Canvas (http://canvas.utexas.edu) 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
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

Homework and Quizzes:

Homework will be assigned regularly, i.e., most every week. Only a portion of the homework problems will be fully graded using a ten point scale, and the rest will be worth five points if completed. For the homework, it is acceptable for groups of students to help each other; however, each student must write up his or her own work. Homework must be turned in by class time on the day it is due. Late homework may be accepted for credit, but only credit for completion can be earned (i.e., a maximum of five points per problem), unless there is a valid health issue. The textbook web site has answers to the exercises.

Homework must be turned in through the online submission system of Canvas. You should write the solutions to the exercises on paper, and then scan the pages in any reasonable format (such as pdf or jpg). Please ensure that your uplodaded document is:

Quizzes will be assigned regularly throughout the semester using the Canvas web site. They will be open book, but they must be completed solely by the individual without help from others. Each quiz must be completed by the date and time specified (late work on quizzes cannot be accepted).


Three in-class exams will be given on Friday Sept. 27, Friday Oct. 25, and Wednesday Nov. 20. A comprehensive final exam will be given Monday, December 16, 2-5:00 p.m.

Final Grade:

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.

The University of Texas at Austin 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."

The University of Texas at Austin 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:

Appropriate academic accommodation for major religious holidays is provided 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.

Counselling 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.