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)

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.
[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 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.
Grading Policy: 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: Statistics for the second midterm test:
Homework assignments
Tentative schedule