MATH 463/663: Advanced Matrix Theory
2019 Spring, University of Nevada, Las Vegas
Instructor: Dr. Le Chen
Email: le.chen@unlv.edu
Office: SEB, 3131
Office Hours: Wed 9:00am-12:00am or by appointment
Class Meeting Times: TuTh 8:30am-9:45am in CBC C110
Discussion Classes: Friday, TBA.
Time period: Jan. 22, 2019 (first lecture) --- May 9, 2019 (last lecture)
Course Description:
Rigorous mathematical treatment of orthogonal matrices, eigenvalues and eigenvectors,
Q-R factorization, singular value decompositions, least-squares fits, generalized inverse,
systems of linear differential equations,
special matrices, matrix operations, matrix derivatives, and matrix inequalities.
Textbook:
[0] Matrix Analysis for Statistics, Third edition, by James R. Schott, Wiley Series in Probability and Statistics. John Wiley & Sons, Inc., Hoboken, NJ, 2017. xiii+520 pp.
Other references:
[1] Matrix Analysis, Second edition by Horn, Roger A. and Johnson, Charles R., Cambridge University Press, Cambridge, 2013. xviii+643.
[2] Topics in matrix analysis in matrix Analysis, by Horn, Roger A. and Johnson, Charles R., Cambridge University Press, Cambridge, 1991. viii+607 pp.
[3] Matrix computations, Third edition, by Golub, Gene H. and Van Loan, Charles F., Johns Hopkins University Press, Baltimore, MD, 1996. xxx+698 pp.
[4] Matrix analysis, by Rajendra Bhatia, Graduate Texts in Mathematics, 169. Springer-Verlag, New York, 1997. xii+347 pp.
Coverage: We will cover most of the following chapters
- Chapter 1 -- A Review of Elemetary Matrix Algebra
- Chapter 2 -- Vector Spaces
- Chapter 3 -- Eigenvalues and Eigenvectors
- Chapter 4 -- Matrix Factorizations and Matrix Norms
- Chapter 5 -- Generalized Inverses
- Chapter 6 -- Systems of Linear Equations
- Chapter 8 -- Special Matrices and Matrix Operations
- Chapter 9 -- Matrix Derivatives and Related Topics
- Chapter 10 --Inequalities
Prerequisite: C or better in either MATH 330 or MATH 365.
Learning Outcomes: By the end of the course, students will be familiar with the basics of matrix algebra including eigenvalues and eigenvectors, be able to compute projection matrices and various decompositions of matrices, be familiar with generalized inverses, and be able to apply the above knowledge to a variety of problems involving systems of linear equations.
Note: The syllabus was created in Sept. 2018, and it is subject to change during the semester.
Homework: Homework will be assigned for each chapter and be collected upon annoucement. Only part of the problem set (randomly chosen) will be graded, however you will receive some credits for completing all homework problems. Please do keep a copy of your homework since it may not return in time.
Quiz: Several quizzes will be given randomly during the semester in the class session.
Attendence: You are expected to attend class regularly. You are responsible for all the materials presented and all the announcements made, if any, at each lecture.
Tests and Final: There will be 2 tests and a cumulative final exam. Failure to take an exam during the scheduled class time will result in a score of zero for that exam. There will be no make-up exam except for well-documented reasons such as a medical emergency. Scientific (non-programmable and non-graphing) calculators are allowed during exams.
- Test 1: Feb. 21, Thursday, in class.
- Test 2: April 4, Thursday, in class.
- Final: May 16, Thursday, 8:00-10:00am.
Grading Policy:
There will be Homework (20%), two tests (25%+25%) , the final exam (30%), plus some bonus points (based on attendance).
- A: 92% -- 100%, A-: 90% -- 91.9%.
- B+: 87% -- 89.9%, B: 82% -- 86.9%, B-: 80% -- 81.9%
- C+: 77% -- 79.9%, C: 72% -- 76.9%, C-: 70% -- 71.9%
- D+: 67% -- 69.9%, D: 62% -- 66.9%, D-: 60% -- 61.9%
- F: 0% -- 59%
Statistics for the first midterm test:
- 90-100: 3.
- 80-89: 1.
- 70-79: 3.
- 60-69: 5.
- 50-59: 5.
- 0-50: 7.
- Absent: 0.
- Total: 34.
Statistics for the second midterm test:
- 90-100: 7.
- 80-89: 2.
- 70-79: 4.
- 60-69: 4.
- 50-59: 0.
- 0-50: 4.
- Absent: 3.
- Total: 24.
Homework assignments
- Chapter 1: 1-7, 9-12, 14-16, 18-28, 30-32, 35, 37, 39, 40. (Due on Feb. 7)
- Chapter 2: 1, 2, 4, 6, 14, 20, 24-26, 30-31, 37-40, 43, 47, 49, 51,53, 54, 57-59. (Due on Feb. 19)
- Chapter 3: 1, 5, 6, 9-11, 14-23, 25, 27, 29, 33-36, 39, 46, 52, 53, 57, 60. (Hints Due on March 26)
- Chapter 4: 1-8, 14, 19-22, 25-28, 32, 34, 37, 39, 41, 42, 44, 46, 47, 49(a). (Hints Due on April 2)
- Chapter 5: 2, 3, 6, 7, 9-13, 16, 34, 35, 38-40, 53, 55. (Hints Due on April 18)
- Chapter 6: 4, 5, 6, 12, 13, 20, 21. (Hints Due on April 25)
- Chapter 8: 1, 4, 7-9, 15, 22, 26-28, 33, 35, 37, 39. (Hints Due on May 2)
- Chapter 9: 2-10, 12. (Hints Due on May 9, optional!)
- Chapter 10: 1-3, 5-7, 10-12, 17, 19-21, 24. (Hints Due on May 9)
Tentative schedule
- Week 1:
- Tuesday, Jan. 22: §1.1 -- §1.5.
- Thursday, Jan. 24: §1.6 -- §1.7.
- Week 2:
- Tuesday, Jan. 29: §1.8 -- §1.9.
- Thursday, Jan. 31: §1.10, §1.11, §2.2.
- Week 3:
- Tuesday, Feb. 5: §2.2 and §2.3.
- Thursday, Feb. 7: §2.4 and §2.5.
- Week 4:
- Tuesday, Feb. 12: §2.6 -- §2.7.
- Thursday, Feb. 14: §2.8 -- §2.10.
- Week 5:
- Tuesday, Feb. 19: Review for Midterm 1.
- Thursday, Feb. 21: (First midterm test)
- Week 6:
- Tuesday, Feb. 26: §3.1 -- §3.3.
- Thursday, Feb. 28: §3.3.
- Week 7:
- Tuesday, Mar. 5: §3.4 and §3.5.
- Thursday, Mar. 7: §3.6 and §3.8.
- Week 8:
- Tuesday, Mar. 12: §3.7 and §3.8.
- Thursday, Mar. 14: §4.1 -- §4.3.
- Week 9:
- Tuesday, Mar. 19: (Spring break)
- Thursday, Mar. 21: (Spring break)
- Week 10:
- Tuesday, Mar. 26: §.4.3 -- §4.5.
- Thursday, Mar. 28: §4.6 -- §4.8.
- Week 11:
- Tuesday, Apr. 2: Review for Midterm 2.
- Thursday, Apr. 4: (Second midterm test)
- Week 12:
- Tuesday, Apr. 9: §5.1 -- §5.4.
- Thursday, Apr. 11: §5.8
- Week 13:
- Tuesday, Apr. 16: §6.1 -- §6.4.
- Thursday, Apr. 18: §6.5 and §6.7.
- Week 14:
- Tuesday, Apr. 23: §8.1 -- §8.4.
- Thursday, Apr. 25: §8.5.
- Week 15:
- Tuesday, Apr. 30: §10.1 -- §10.2.
- Thursday, May 2: §10.2.
- Week 16:
- Tuesday, May 7: §10.3, §10.4 and §10.6.
- Thursday, May 9: Review and §8.9 and §8.10 for bonus points.
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sability Resource Center (SSC-A 143, http://drc.unlv.edu/, 702-895-0866) provides resources for students with disabilities. If you feel that you have a disability, please make an appointment with a Disabilities Specialist at the DRC to discuss what options may be available to you. If you are registered with the UNLV Disability Resource Center, bring your Academic Accommodation Plan from the DRC to the instructor during office hours so that you may work together to develop strategies for implementing the accommodations to meet both your needs and the requirements of the course. Any information you provide is private and will be treated as such. To maintain the confidentiality of your request, please do not approach the instructor in front of others to discuss your accommodation needs.
Religious Holiday Policy:
ny student missing class quizzes, examinations, or any other class or lab work because of observance of religious holidays shall be given an opportunity during that semester to make up missed work. The make-up will apply to the religious holiday absence only. It shall be the responsibility of the student to notify the instructor no later than the end of the first two weeks of classes, January 26, 2018, of his or her intention to participate in religious holidays which do not fall on state holidays or periods of class recess. For additional information, please visit: http://catalog.unlv.edu/content.php?catoid=6&navoid=531.
Incomplete Grades:
The grade of I -- Incomplete -- can be granted when a student has satisfactorily completed three-fourths of course work for that semester/session but for reason(s) beyond the student's control, and acceptable to the instructor, cannot complete the last part of the course, and the instructor believes that the student can finish the course without repeating it. The incomplete work must be made up before the end of the following regular semester for undergraduate courses. Graduate students receiving "I" grades in 500-, 600-, or 700-level courses have up to one calendar year to complete the work, at the discretion of the instructor. If course requirements are not completed within the time indicated, a grade of F will be recorded and the GPA will be adjusted accordingly. Students who are fulfilling an Incomplete do not register for the course but make individual arrangements with the instructor who assigned the I grade.
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