MATH 463/663: Advanced Matrix Theory
2019 Spring, University of Nevada, Las Vegas
Instructor: Dr. Le Chen
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)
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.
 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.
 Matrix Analysis, Second edition by Horn, Roger A. and Johnson, Charles R., Cambridge University Press, Cambridge, 2013. xviii+643.
 Topics in matrix analysis in matrix Analysis, by Horn, Roger A. and Johnson, Charles R., Cambridge University Press, Cambridge, 1991. viii+607 pp.
 Matrix computations, Third edition, by Golub, Gene H. and Van Loan, Charles F., Johns Hopkins University Press, Baltimore, MD, 1996. xxx+698 pp.
 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
Prerequisite: C or better in either MATH 330 or MATH 365.
- 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
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.
There will be Homework (20%), two tests (25%+25%) , the final exam (30%), plus some bonus points (based on attendance).
Statistics for the first midterm test:
- 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 second midterm test:
- 90-100: 3.
- 80-89: 1.
- 70-79: 3.
- 60-69: 5.
- 50-59: 5.
- 0-50: 7.
- Absent: 0.
- Total: 34.
- 90-100: 7.
- 80-89: 2.
- 70-79: 4.
- 60-69: 4.
- 50-59: 0.
- 0-50: 4.
- Absent: 3.
- Total: 24.
- 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)
- 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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