spring 2022: M340L matrices and matrix calculations
Course Syllabus: M340L — Spring 2022
Contact: office hours: TTh 1:00 pm — 2:00 pm
email: jwchong 🍎 math 🐶 utexas 🐶 edu
office: RLM 12.140
Teaching Assistant: Kendric Schefers
Lecture: MWF 11:00 am — 12:00 pm in RLP 0.126
January 19 — May 6
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)
- Mathematics for Machine Learning by M. P. Deisenroth, A. A. Faisal, and C. S. Ong (Reference) The pdf of this book is actually freely available online.
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 will be assigned regularly from the course textbook along with problems from the instructor. There will be a total of 11 assignments throughout the semester. Each problem set is assigned 50 points and 10-12 problems will be randomly selected problems for grading. We drop the lowest score. It is acceptable for groups of students to discuss the problems with each other; however, each student must write up his or her own solutions. See the tentative schedule for the due dates. Every assignment is due at 11:59 PM (CST) on the indicated date. Late assignments will not be accepted.
Submission: All homework should be submitted through Gradescope.
Gradescope: All your assignments needs to be submitted through Gradescope. View the LINK for more information on how to submit your work electronically.
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.
Exams: There will be three 50-minute in-class exams. The dates of the exams are
- Exam 1: Wed, Feb. 16
- Exam 2: Wed, Mar. 23
- Exam 3: Wed, Apr. 27
Final Exam: There will be a 3-hour in-class final exam. The final exam is cumulative.
- Final Exam: Mon. May. 16, 9:00am — 12:00pm
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: Course grades will be computed based on your homeworks, in-class exams and the final exam grades. Your course grade will be determined by the best of the following two weighted averages:
- 30% Homework, 45% Exams (15% per Exam), 25% Final,
- 30% Homework, 30% Exams (15% per Exam), 40% 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.
| Date | Reading | Additional Practice Problems | |
|---|---|---|---|
| W 1/19 | Lecture 1: Systems of Linear Equations | § 1.1 | § 1.1: #3,4,5,7,13,17,18,21,23-25, 27,28,33 |
| F 1/21 | Lecture 2: Row Reduction | § 1.2 | § 1.2: #3,6,9,13,15,20,21-22,25-26,32-34 |
| M 1/24 | Lecture 3: Vector Equations | § 1.3 | § 1.3: #12,14,17,19,22-25,29 |
| W 1/26 | 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 1/28 | Lecture 5: Solution Sets of Linear Systems (HW1 Due) | § 1.5 | § 1.5: #2,6,12-13,23-24,30-31,36-38 |
| M 1/31 | Lecture 6: Linear Independence | § 1.7 | § 1.7: #6-7,10,18,20-22,26-30,38-40,42,44 |
| W 2/2 | 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 2/4 | Lecture 8: The Matrix of a Linear Transformation (HW2 Due) | § 1.9 | § 1.9: #2,3,6-10,14,23-24,26,28,31-32,35, 37,40 |
| M 2/7 | Lecture 9: Matrix Operations | § 2.1 | § 2.1: #7,9-12,15-16,23-24,34-38,40 |
| W 2/9 | Lecture 10: The Inverse of a Matrix | § 2.2 | § 2.2: #2,9-10,12-14,20-22,31,33,35-36,41 |
| F 2/11 | Lecture 11: Characterizations of Invertible Matrices (HW 3 Due) | § 2.3 | § 2.3: #6,11-12,14-15,22,27-28,30,32, 41-42,44-45 |
| M 2/14 | Lecture 12: Partitioned Matrices | § 2.4 | § 2.4: #8,10,14-16,18,21,25-27 |
| W 2/16 | Exam 1: § 1.1-1.5, 1.7-1.9, and 2.1-2.3 | Sample Exam 1 | |
| F 2/18 | Lecture 13: Matrix Factorizations | § 2.5 | § 2.5: #2,13,18-19,22-26,31-32 |
| M 2/21 | Lecture 14: Introduction to Determinants | § 3.1 | § 3.1 #2,14,22,24,39-40,43-46 |
| W 2/23 | 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 2/25 | Lecture 16: Vector Spaces and Subspaces (HW 4 Due) | § 4.1 | § 4.1: #2,3,7-8,11,21-24,26,32,33,38 |
| M 2/28 | Lecture 17: Null Spaces, Column Spaces, and Linear Transformations | § 4.2 | § 4.2: #6,10,12,24-26,30,32-33,38-39 |
| W 3/2 | Lecture 18: Linearly Independent Sets; Bases | § 4.3 | § 4.3: #4-5,10,14,18,21-22,26,31-32, 38 |
| F 3/4 | Lecture 19: Coordinate Systems (HW 5 Due) |
§ 4.4 | § 4.4: #3,8,10,13,15-16,25-26,28,32,34,36 |
| M 3/7 | Lecture 20: The Dimension of a Vector Space and Rank | § 4.5-4.6 | § 4.5: #8,14,19-20,22,24,29-30,33-34 § 4.6: #4,6,10,22,24,17-18,27-29,36,38 |
| W 3/9 | Lecture 21: Change of Basis | § 4.7 | § 4.7: #2,4,6,8,11-12,14,17 |
| F 3/11 | Lecture 22: Eigenvectors and Eigenvalues (HW 6 Due) | § 5.1 | § 5.1: #4,8,13,16,18,21-22,26-27,29-30,32,40 |
| M 3/14 | Spring Break |
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| W 3/16 | Spring Break |
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| F 3/18 | Spring Break |
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| M 3/21 | Lecture 23: The Characteristic Equation | § 5.2 | § 5.2: #4,12,18,21-22,24,27-28,30 |
| W 3/23 | Exam 2: § 2.4-2.5, 3.1-3.2, and 4.1-4.7 | Sample Exam 2 | |
| F 3/25 | Lecture 24: Diagonlization | § 5.3 | § 5.3: #2,5,10,18,21-22,24,28,31,36 |
| M 3/28 | Lecture 25: Eigenvectors and Linear Transformations | § 5.4 | § 5.4: #2,6,10,12,14,17,20,27-28,30,32 |
| W 3/30 | Lecture 26: Complex Eigenvalues | § 5.5 | § 5.5: #4,10,16,23-26,28 |
| F 4/1 | Lecture 27: Applications to Markov Chains (HW 7 Due) | § 4.9 | § 4.9: #2,12,16-17,19-20,21-22 |
| M 4/4 | Lecture 28: Random Walks | § 10.1 | § 10.1: #14,16,20-22,26,27 |
| W 4/6 | Lecture 29: Google's PageRank | § 10.2 | § 10.2: #8,11-12, 14,16-17,20-22,26,35,37 |
| F 4/8 | Lecture 30: Inner Product, Length, and Orthogonality (HW 8 Due) | § 6.1 | § 6.1: #6,14,19-20,24,26,28,30-31,34 |
| M 4/11 | Lecture 31: Orthogonal Sets | § 6.2 | § 6.2 #10,12,17,23-24,27-30,35-36 |
| W 4/13 | Lecture 32: Orthogonal Projections | § 6.3 | § 6.3: #4,10,12,15,17,21-22,25-26 |
| F 4/15 | Lecture 33: The Gram-Schmidt Process (HW 9 Due) |
§ 6.4 | § 6.4: 12,14,16-18,24-26 |
| M 4/18 | Lecture 34: Least-Squares Problems | § 6.5 | § 6.5: #4,6,8,12,16-20 |
| W 4/20 | Lecture 35: Applications to Linear Models | § 6.6 | § 6.6: #1-4 |
| F 4/22 | Lecture 36: Diagonalization of Symmetric Matrices (HW 10 Due) | § 7.1 | § 7.1 #22,24-26,30,32,34-36,40 |
| M 4/25 | Lecture 37: Quadratic Forms | § 7.2 | § 7.2 #6,8,10,16,21-22,24-28 |
| W 4/27 | Exam 3: § 5.1-5.5, 4.9, 10.1-10.2, 6.1-6.6 | Sample Exam 3 | |
| F 4/29 | Lecture 38: The Singular Value Decomposition | § 7.4 | § 7.4 #10,12,13,16,18,21-22,26,28-29 |
| M 5/2 | Lecture 39: The Singular Value Decomposition Cont'd | § 7.4 | |
| W 5/4 | Lecture 40: Applications to Image Processing and Statistics | § 7.5 | |
| F 5/6 | Lecture 41: Applications to Image Processing and Statistics Cont'd (HW 11 Due) |
§ 7.5 | |
| M 5/16 | 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.)
Downloading MATLAB: To install MATLAB onto your personal devices (laptops and desktops), please follow the instructions on this page to submit a request to download the program. Once you submit a request, you should receive an email (within a few minutes) on your university email account. Follow the instructions on the email to complete the installation.
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
