spring 2020: M340L matrices and matrix calculations
Course Syllabus: M340L-Spring 2020
Contact: office hours: TTh 2:00 pm-3:00 pm
email: jwchong[at]math[dot]utexas[dot]edu
office: RLM 12.140
Teaching Assistant: Kendric D. Schefers
Lecture: MWF 4:00 pm-5:00 pm in
Zoom Meeting, January 21 - May 8
Textbook: There is one required textbook listed for the course. I have also included additional reference textbooks for interested students.
- Linear Algebra and Its Applications, 5th edition by D. Lay, S. Lay, and J. McDonald (Required)
- Linear Algebra and Its Applications, 4th edition by Gilbert Strang, (Reference)
- Linear Algebra and Learning from Data by Gilbert Strang. (Reference)
- Fundamentals of Matrix Computations, 3rd edition by David Watkins, (Reference)
- Matrix Analysis, 2nd edition by R. Horn and C. Johnson, (Reference)
Prerequisites: Student must have earned at least a C- in Mathematics 408C, 408K, or 408N (Calculus I) or any equivalent course.
Course Description: The goal of M340L is to present the many uses of matrices and the many techniques and concepts needed in such uses. The emphasis is on concrete concepts and understanding and using techniques, rather than on learning proofs and abstractions. The course is designed for applications-oriented students such as those in the natural and social sciences, engineering, and business. Topics might include matrix operations, systems of linear equations, introductory vector-space concepts (e.g., linear dependence and independence, basis, dimension), determinants, introductory concepts of eigensystems, introductory finite state Markov chains, and least square problems. Credit will be granted for only one of the following: M340L or M341.
Homework: Homework problems along with suggested exercises will be assigned regularly from the course textbook. There will be a total of
Participation: To encourage active online learning, 5% of your grade will be dedicatedto class participation. There are a few forms of class participation: (1) asking courserelevant questions on Piazza (2) answering questions on Piazza (3) asking questions duringInstructor/ TA office hours (4) answering zoom polls during lectures. For each action,you will receive a point. You will need 10 points to earn the 5% participation grade.
Course Readings: Reading the sections of the textbook corresponding to the assigned homework exercises is considered part of the homework assignment. You are responsible for material in the assigned reading whether or not it is discussed in the lecture.
Online Quizzes: There will be six online quizzes administered through canvas. Each quiz will be 25-30 minutes in length.
In-class Exams: There will be
Take-Home Exams: There will be two take-home exams to replace in-class Exam 2 and Exam 3. Each take-home exam is given approximately a week to complete. Submission: All take-home exams should be submitted through gradescope.
Final Exam:
Make-up Policy: Make-ups for in-class exams will only be given in the case of a documented absence due to illness, religious observance, participation in a University activity at the request of University authorities, or other compelling circumstances.
Grading:
- 15% Homework, 10% MATLAB, 45% Exams (15% per Exam), 30% Final,
- 15% Homework, 10% MATLAB, 30% Exams (Drop lowest exam score, 15% per Exam), 45% Final.
- 15% Homework, 10% MATLAB, 5% Participation, 15% Quizzes, 30% Exams (10% per Exam), 25% Final,
- 15% Homework, 10% MATLAB, 5% Participation, 15% Quizzes, 20% Exams (Drop lowest exam score, 10% per Exam), 35% Final.
| A | A- | B+ | B | B- | C+ | C | C- |
|---|---|---|---|---|---|---|---|
| >92 | 92-90 | 89-87 | 86-83 | 82-80 | 79-77 | 76-73 | 72-70 |
It is possible that the cutoffs may be lower at the discretion of the instructor. However, students who get less than 50% of the maximum possible number of points will automatically receive an F for the course.
Students with Disabilities: Students with disabilities may request appropriate accommodations from the Division of Diversity and Community Engagement, Services for Students with Disabilities (SSD), 512-471-6259, https://diversity.utexas.edu/disability/ . Notify your instructor early in the semester if accommodation is required.
Academic Integrity: Each student in the course is expected to abide by the University of Texas 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.” You are expected to read carefully and adhere to the following instruction provided by the Office of the Dean of Students: http://deanofstudents.utexas.edu/conduct/academicintegrity.php
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, website www.cmhc.utexas.edu. Your mental health should be your top priority, so please take good care of yourself.
Tentative Schedule and Suggested Homework: Below is a tentative schedule of the course with the material that I hope to cover and when. This will undoubtedly change as we progresses through the semester, so check here often for updates. However, I will try my best to follow the schedule religiously. The reading and homework are from Lay.
Important Updates: Due to the onset of the Coronavirus and the extension of the UT spring break, I have made significant changes to our schedule for the remainder of the semester. Updated on March 31, 2020.
| Date | Reading | Homework/Suggested Problems | |
|---|---|---|---|
| W 1/22 | Lecture 1: Systems of Linear Equations | § 1.1 | § 1.1: #3,4,5,7,13,17,18,21,23-25, 27,28,33,34 |
| F 1/24 | Lecture 2: Row Reduction | § 1.2 | § 1.2: #3,6,9,13,15,20,21-22,25-26,32-34 HW 1 |
| M 1/27 | Lecture 3: Vector Equations (HW1 Due) |
§ 1.3 | § 1.3: #12,14,17,19,22-25,29 |
| W 1/29 | Lecture 4: The Matrix Equations Ax=b | § 1.4 | § 1.4: #1,4,9,13,15,17,19,23-24,31-32,40,42 |
| F 1/31 | Lecture 5: Solution Sets of Linear Systems | § 1.5 | § 1.5: #2,6,12-13,23-24,30-31,36-38 HW 2 |
| M 2/3 | Lecture 6: Linear Independence (HW2 Due) |
§ 1.7 | § 1.7: #6-7,10,18,20-22,26-30,38-40,42,44 |
| W 2/5 | Lecture 7: Introduction to Linear Transformation | § 1.8 | § 1.8: #4,8,10,12,15-16,19-22,25,31-32,34,38,40 |
| F 2/7 | Lecture 8: The Matrix of a Linear Transformation | § 1.9 | § 1.9: #2,3,6-10,14,23-24,26,28,31-32,35, 37,40 HW 3 |
| M 2/10 | Lecture 9: Matrix Operations (HW3 Due) |
§ 2.1 | § 2.1: #7,9-12,15-16,23-24,34-38,40 |
| W 2/12 | Lecture 10: The Inverse of a Matrix | § 2.2 | § 2.2: #2,9-10,12-14,20-22,31,33,35-36,41 |
| F 2/14 | Lecture 11: Characterizations of Invertible Matrices (ML1 Due) | § 2.3 | § 2.3: #6,11-12,14-15,22,27-28,30,32, 41-42,44-45 HW 4 |
| M 2/17 | Exam 1: § 1.1-1.5, 1.7-1.9, and 2.1-2.3 | Sample Exam 1 | |
| W 2/19 | Lecture 12: Partitioned Matrices (HW4 Due) |
§ 2.4 | § 2.4: #8,10,14-16,18,21,25-27 |
| F 2/21 | Lecture 13: Matrix Factorizations | § 2.5 | § 2.5: #2,13,18-19,22-26,31-32 HW 5 |
| M 2/24 | Lecture 14: Introduction to Determinants (HW5 Due) |
§ 3.1 | § 3.1 #2,14,22,24,39-40,43-46 |
| W 2/26 | Lecture 15: Properties of Determinants | § 3.2 | § 3.2: #14,22,27-28,33,36,40,45-46 Ch 3 Suppl. Ex.: #14,15,16,19,20 |
| F 2/28 | Lecture 16: Vector Spaces and Subspaces | § 4.1 | § 4.1: #2,3,7-8,11,21-24,26,32,33,38 HW 6 |
| M 3/2 | Lecture 17: Null Spaces, Column Spaces, and Linear Transformations (HW6 Due) |
§ 4.2 | § 4.2: #6,10,12,24-26,30,32-33,38-39 |
| W 3/4 | Lecture 18: Linearly Independent Sets; Bases | § 4.3 | § 4.3: #4-5,10,14,18,21-22,26,31-32, 38 |
| F 3/6 | Lecture 19: Coordinate Systems | § 4.4 | § 4.4: #3,8,10,13,15-16,25-26,28,32,34,36 HW 7 |
| M 3/9 | Lecture 20: The Dimension of a Vector Space (HW7 Due) |
§ 4.5 | § 4.5: #8,14,19-20,22,24,29-30,33-34 |
| W 3/11 | Lecture 21: Rank | § 4.6 | § 4.6: #4,6,10,22,24,17-18,27-29,36,38 |
| F 3/13 | (ML2 Due) |
§ 4.7 | § 4.7: #2,4,6,8,11-12,14,17 HW 8 |
| M 3/16 | Spring Break |
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| W 3/18 | Spring Break |
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| F 3/20 | Spring Break |
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| M 3/23 | Spring Break |
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| W 3/25 | Spring Break |
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| F 3/27 | Spring Break |
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| M 3/30 | Lecture 22: Change of Basis (HW8 Due) |
§ 4.7 | § 4.7: #2,4,6,8,11-12,14,17 |
| W 4/1 | Lecture 23: Eigenvectors and Eigenvalues | § 5.1 | § 5.1: #4,8,13,16,18,21-22,26-27,29-30,32,40 |
| F 4/3 | Lecture 24: The Characteristic Equation (Q1 Due) |
§ 5.2 | § 5.2: #4,12,18,21-22,24,27-28,30 |
| M 4/6 | Lecture 25: Diagonlization (TH 2 Due) |
§ 5.3 | § 5.3: #2,5,10,18,21-22,24,28,31,36 |
| W 4/8 | Lecture 26: Eigenvectors and Linear Transformations (Q2 Due Th 4/9) | § 5.4 | § 5.4: #2,6,10,12,14,17,20,27-28,30,32 |
| F 4/10 | Lecture 27: Complex Eigenvalues | § 5.5 | § 5.5: #4,10,16,23-26,28 HW 09 |
| M 4/13 | Lecture 28: Applications to Markov Chains (HW 09 Due, Q3 Due Tu 4/14) |
§ 4.9 | § 4.9: #2,12,16-17,19-20,21-22 |
| W 4/15 | Lecture 29: Random Walks | § 10.1 | § 10.1: #14,16,20-22,26,27 |
| F 4/17 | Lecture 30: Google's PageRank | § 10.2 | § 10.2: #8,11-12, 14,16-17,20-22,26,35,37 |
| M 4/20 | Lecture 31: Inner Product, Length, and Orthogonality (ML3 Due, Q4 Due Tu 4/21) | § 6.1 | § 6.1: #6,14,19-20,24,26,28,30-31,34 |
| W 4/22 | Lecture 32: Orthogonal Sets | § 6.2 | § 6.2 #10,12,17,23-24,27-30,35-36 |
| F 4/24 | Lecture 33: Orthogonal Projections | § 6.3 | § 6.3: #4,10,12,15,17,21-22,25-26 HW 10 |
| M 4/27 | Lecture 34: The Gram-Schmidt Process (HW10 Due, Q5 Due Tu 4/28) |
§ 6.4 | § 6.4: 12,14,16-18,24-26 |
| W 4/29 | Lecture 35: Least-Squares Problems | § 6.5/6.6 | § 6.5: #4,6,8,12,16-20 § 6.6: #1-4 |
| F 5/1 | Lecture 36: Diagonalization of Symmetric Matrices | § 7.1 | § 7.1 #22,24-26,30,32,34-36,40 |
| M 5/4 | Lecture 37: Quadratic Forms (TH 3 Due) |
§ 7.2 | § 7.2 #6,8,10,16,21-22,24-28 |
| W 5/6 | Lecture 38: The Singular Value Decomposition (Q6 Due Th 5/7) | § 7.4 | § 7.4 #10,12,13,16,18,21-22,26,28-29 |
| F 5/8 | Lecture 39: The Singular Value Decomposition Cont'd (ML4 Due Monday 5/11) |
§ 7.4 | |
| M 5/11 | Optional Final Review Session | ||
| F 5/15 | Final Exam | ||
Why MATLAB?: MATLAB stands for MATrix LABoratory. Originally written by Cleve Moler for college linear algebra courses, MATLAB has evolved into a high-level language and interactive environment for linear algebra computations in science and industry all over the world. Using MATLAB in this course will save you time on homework, help you learn linear algebra, and give you a glimpse of how linear algebra is applied in practical work. Another purpose of introducing MATLAB in this course is to help you obtain a working knowledge with the software for future courses. (Programming experiences is not required.)
MATLAB Projects: There will be four MATLAB projects worth 25 points each. These will be posted below as they become available. Projects also include some instructional introductions. Like homework, it is acceptable for groups of students to discuss the problems with each other; however, each student must write up his or her own code/work.
- MATLAB Project 1 Due Feb. 14
- MATLAB Project 2 Due Mar. 13, Attachment File download here
- MATLAB Project 3 Due Apr. 15
- MATLAB Project 4 Due May 8
MATLAB Problems Formatting: Your MATLAB project should be formated as in this example. Your homework should clearly display the answer to each MATLAB problem. Moreover, you should suppress any unnecessary output to keep your page count to the bare minimum. Moreover, please use double-sided printing to minimize paper waste. The m-file template for the above example can be download here. (No Extra Credit, the file was from a previous class)
I have included links to relevant MATLAB tutorials:
- Publish your m-file as an html file: https://www.mathworks.com/videos/publishing-matlab-code-from-the-editor-101570.html
- Important linear algebra Matlab programs: https://www.mathworks.com/help/matlab/linear-algebra.html
Computer Lab: If you do not already have MATLAB installed on your personal computer, you could go to the Undergraduate Computer Lab (RLM 7.122) and sign-up for an account to access the computers in the lab, which all have MATLAB installed. The lab is accessible whenever the RLM building is accessible. Current RLM operating hours are:
- M-Th: 6:00am -- 11:00pm
- F: 6:00am -- 10:00pm
- Sat: 6:00am -- 5:00pm
- Sun: 2:00pm -- 11:00pm
