fall 2019: M340L Matrices and Matrix Calculations
Course Syllabus: M340L-Fall 2019
Contact: office hours: TTh 2:00 pm-3:00 pm
email: jwchong[at]math[dot]utexas[dot]edu
office: RLM 12.140
Teaching Assistant: Kyrylo Muliarchyk
Lecture: MWF 4:00 pm-5:00 pm in PHR 2.110,
August 28 - December 9
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)
- Fundamentals of Matrix Computations, 3rd edition by David Watkins, (Reference)
- Matrix Analysis, 2nd edition by R. Horn and C. Johnson, (Reference)
- Linear Algebra and Its Applications, 2nd edition by Peter Lax. (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. Every assignment will have at least one marked problem which requires computer assistance. You are required to solve these marked problems with MATLAB. See below for more information. There will be a total of 14 assignments throughout the semester. We will drop the two lowest scores. It is acceptable for groups of students to help each other on the homework sets; however, each student must write up his or her own work. See the tentative schedule for the assignments and due dates. Every assignment is due before lecture on the indicated dates. Late assignments will not be accepted.
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.
In-class Exams: There will be three 50-minute in-class exams. The dates of the exams are Sept. 23, Oct. 21, and Nov. 15.
Final Exam: The final exam is cumulative. The duration of the final exam is 3 hours. The date of the final exam: Friday, Dec. 13, 7pm-10pm. Final Exam Location: TBA.
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 based on homeworks, in-class exams, and the final exam. Your course grade will be determined by the best of the following two weighted averages:
- 25% Homework, 45% Exams (15% per Exam), 30% Final,
- 25% Homework, 30% Exams (Drop lowest exam score, 15% per Exam), 45% Final.
| A+ | A | A- | B+ | B | B- | C+ | C | C- |
|---|---|---|---|---|---|---|---|---|
| 100-97 | 96-93 | 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 | Homework/Suggested Problems | |
|---|---|---|---|
| W 8/28 | Lecture 1: Systems of Linear Equations and Row Reduction |
§ 1.1-1.2 | § 1.1: #5,7,13,17,23-25,28,33,34 § 1.2: #3,6,9,13,21-22,25,32-34 |
| F 8/30 | Lecture 2: Vector Equations | § 1.3 | § 1.3: #12,14,17,19,22-25 HW 1 |
| M 9/2 | Labor Day | ||
| W 9/4 | Lecture 3: The Matrix Equations Ax=b (HW1 Due) |
§ 1.4 | § 1.4: #1,4,9,13,15,17,19,23-24,31-32,40,42 |
| F 9/6 | Lecture 4: Solution Sets of Linear Systems | § 1.5 | § 1.5: #2,6,12-13,23-24,30-31,36-38 HW 2 |
| M 9/9 | Lecture 5: Linear Independence (HW2 Due) |
§ 1.7 | § 1.7: #6-7,10,18,20-22,27-30,38-40,42,44 |
| W 9/11 | Lecture 6: Introduction to Linear Transformation | § 1.8 | § 1.8: #4,8,10,12,15-16,19-22,25,31-32,34,38,40 |
| F 9/13 | Lecture 7: The Matrix of a Linear Transformation | § 1.9 | § 1.9: #2,3,8-10,14,23-24,26,28,31-32,35, 37,40 HW 3 |
| M 9/16 | Lecture 8: Matrix Operations (HW3 Due) |
§ 2.1 | § 2.1: #7,9-12,15-16,23-24,34-38,40 |
| W 9/18 | Lecture 9: The Inverse of a Matrix | § 2.2 | § 2.2: #2,9-10,12-14,20-22,31,33,35-36,41 |
| F 9/20 | Lecture 10: Characterizations of Invertible Matrices | § 2.3 | § 2.3: #6,11-12,14-15,22,27-28,30,32, 41-42,44-45 HW 4 |
| M 9/23 | Exam 1: § 1.1-1.5, 1.7-1.9, and 2.1-2.3 | Sample Exam 1 | |
| W 9/25 | Lecture 11: Partitioned Matrices (HW4 Due) |
§ 2.4 | § 2.4: #10,14-15,18,21,26-27 |
| F 9/27 | Lecture 12: Matrix Factorizations | § 2.5 | § 2.5: #2,13,18-19,25-26,31-32 HW 5 |
| M 9/30 | Lecture 13: Introduction to Determinants (HW5 Due) |
§ 3.1 | § 3.1 #2,14,22,24,39-40,43-46 |
| W 10/2 | Lecture 14: 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 10/4 | Lecture 15: Vector Spaces and Subspaces | § 4.1 | § 4.1: #2,3,7-8,11,21-24,26,32,33,38 HW 6 |
| M 10/7 | Lecture 16: Null Spaces, Column Spaces, and Linear Transformations (HW6 Due) |
§ 4.2 | § 4.2: #6,10,12,24-26,30,32-33,38-39 |
| W 10/9 | Lecture 17: Linearly Independent Sets; Bases | § 4.3 | § 4.3: #4-5,10,14,18,21-22,26,31-32, 38 |
| F 10/11 | Lecture 18: Coordinate Systems | § 4.4 | § 4.4: #3,8,10,13,15-16,25-26,28,32,34,36 HW 7 |
| M 10/14 | Lecture 19: The Dimension of a Vector Space (HW7 Due) |
§ 4.5 | § 4.5: #8,14,19-20,22,24,29-30,33-34 |
| W 10/16 | Lecture 20: Rank | § 4.6 | § 4.6: #4,6,10,22,24,17-18,27-29,36,38 |
| F 10/18 | Lecture 21: Change of Basis | § 4.7 | § 4.7: #2,4,6,8,11-12,14,17 HW 8 |
| M 10/21 | Exam 2: § 2.4-2.5, 3.1-3.2, and 4.1-4.6 | Sample Exam 2 | |
| W 10/23 | Lecture 22: Eigenvectors and Eigenvalues (HW8 Due) |
§ 5.1 | § 5.1: #4,8,13,16,18,21-22,26-27,29-30,32,40 |
| F 10/25 | Lecture 23: The Characteristic Equation | § 5.2 | § 5.2: #4,12,18,21-22,24,27-28,30 HW 9 |
| M 10/28 | Lecture 24: Diagonlization |
§ 5.3 | § 5.3: #2,5,10,18,21-22,24,28,31,36 |
| W 10/30 | Lecture 25: Eigenvectors and Linear Transformations (HW9 Due) |
§ 5.4 | § 5.4: #2,6,10,12,14,17,20,27-28,30,32 |
| F 11/1 | Lecture 26: Complex Eigenvalues | § 5.5 | § 5.5: #4,10,16,23-26,28 HW 10 |
| M 11/4 | Lecture 27: Applications to Markov Chains (HW10 Due) |
§ 4.9 | § 4.9: #2,12,16-17,19-20,21-22 |
| W 11/6 | Lecture 28: Random Walks | § 10.1 | § 10.1: #14,16,20-22,26,27 |
| F 11/8 | Lecture 29: Google's PageRank | § 10.2 | § 10.2: #8,11-12, 14,16-17,20-22,26,35,37 HW 11 |
| M 11/11 | Lecture 30: Inner Product, Length, and Orthogonality (HW11 Due) |
§ 6.1 | § 6.1: #6,14,19-20,24,26,28,30-31,34 |
| W 11/13 | Lecture 31: Orthogonal Sets | § 6.2 | § 6.2 #10,12,17,23-24,27-30,35-36 HW 12 |
| F 11/15 | Exam 3: § 4.7, 4.9, 5.1-5.5, 5.8, 10.1-10.2 | Sample Exam 3 | |
| M 11/18 | Lecture 32: Orthogonal Projections (HW12 Due) |
§ 6.3 | § 6.3: #4,10,12,15,17,21-22,25-26 |
| W 11/20 | Lecture 33: The Gram-Schmidt Process | § 6.4 | § 6.4: 12,14,16-18,24-26 |
| F 11/22 | Lecture 34: Least-Squares Problems | § 6.5/6.6 | § 6.5: #4,6,8,12,16-20 § 6.6: #1-4 HW 13 |
| M 11/25 | Lecture 35: Diagonalization of Symmetric Matrices (HW13 Due) |
§ 7.1 | § 7.1 #22,24-26,30,32,34-36,40 |
| W 11/27 | Thanksgiving Break | ||
| F 11/29 | Thanksgiving Break | ||
| M 12/2 | Lecture 36: Quadratic Forms | § 7.2 | § 7.2 #6,8,10,16,21-22,24-28 |
| W 12/4 | Lecture 37: The Singular Value Decomposition | § 7.4 | § 7.4 #10,12,13,16,18,21-22,26,28-29 |
| F 12/6 | Lecture 38: Principal Component Analysis (PCA) | § 7.5 | § 7.5 #2,4,8,9 HW 14 |
| M 12/9 | Lecture 39: Final Review (HW14 Due) |
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| F 12/13 | Final Exam |
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MATLAB Problems: Your MATLAB 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
