Math 464/514 - Applied Matrix Theory, Fall 2017

This course along with Math 504 prepares graduate students for the Numerical Analysis Qualifying Exam.
Time: Tue & Thur 9:30-10:45 a.m., Centennial Engineering Center 1028
Instructor Info: Anna Skripka, skripka [at] math [dot] unm [dot] edu
Prerequisite: Math 314 or 321
Lecture notes by Jens Lorenz
Textbook for supplementary reading: Carl D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM, 2000.
Office hours in SMLC 212: Tue and Thur 11 a.m. - noon, and also by appointment
Grades will be based on homework.
Homework is to be posted on UNM Learn.


Aug 22, 24:      Review. Gaussian elimination without interchanges. LU factorization.
(Lecture notes 1.1, 1.4. Textbook 1.2, 1.3, 1.5, 3.2, 3.5, 3.6, 3.7, 3.9, 3.10.)
HW1 due August 31 is posted on UNM Learn.
Aug 29, 31:      Gaussian elimination with partial pivoting. Factorization PA=LU and its applications.
(Lecture notes 1.5-1.8, 1.3. Textbook 3.8, 1.4.)
HW2 due September 7 is posted on UNM Learn.
Sep 5, 7:      Norms and inner products. Conditioning of linear systems.
(Lecture notes 2.1-3.1. Textbook 3.10, 5.1, 5.2, 5.3.)
HW3 due September 14
Sep 12, 14:      Fundamental subspaces of a rectangular matrix. Orthogonal complements.
(Lecture notes 4.1-4.5. Textbook 4.1-4.4, 5.11.)
HW4 due September 21
Sep 19, 21:      Direct sums, projections. Least squares problems and their applications.
(Lecture notes 5.1-5.4, 7.1, 7.2, 3.2. Textbook 5.9, 5.13.)
HW5 due September 28
Sep 26, 28:      Gram-Schmidt orthogonalization, QR factorization. Householder reduction.
(Lecture notes 7.3-7.6. Textbook 5.5, 5.6, 5.7.)
HW6 due October 10
Oct 3, 5:      Singular value decomposition. Applications to least squares problems. Pseudoinverse.
(Lecture notes 8.1-8.3. Textbook 5.12.)
Oct 10:      Frobenius norm. SVD, rank, condition number. Application to information storage.
(Lecture notes 8.4, 8.5, 2.2. Textbook 5.12.)
HW7 due October 19
Oct 17, 19:      Sign of a permutation. Determinant.
(Lecture notes 9.1, 9.3. Textbook 6.1.)
Oct 24, 26:      Properties and applications of determinants. Connection to volumes.
(Lecture notes 9.4, 9.2. Textbook 6.1, 6.2.)
HW8 due November 2
Oct 31, Nov 2:      Eigenvalues and eigenvectors. Schur decomposition. Diagonalization of a normal matrix.
(Lecture notes 9.5, 9.7, 10.1-10.5. Textbook 7.1, 7.2, 7.5.)
HW9 due November 9
Nov 7, 9:      Matrix exponential. Systems of differential equations. Stability, separation of variables.
(Lecture notes 10.6, 11.1, 11.2. Textbook 7.3, 7.4.)
HW10 due November 16
Nov 14, 16:      Jordan normal form.
(Lecture notes 12.1-12.5. Textbook 7.7, 7.8.)
Nov 21:      Limiting behaviour of matrix powers and matrix exponential.
(Lecture notes 12.6, 12.7.)
HW11 due November 30
Nov 28, 30:      Minimal polynomials. Krylov subspace methods. GMRES. Gradient method.
(Lecture notes 15.1-15.4. Textbook 7.11.)
Dec 5, 7:      Conjugate gradient method. Review.
(Textbook 7.11.)
Optional Final Exam: Dec 12 (Tuesday), 12:30 - 2:30 pm, DSH 232.
Regrade Policy
If you think you deserve more points for your work, then you need to request a regrade within a week after the day the assignment is distributed in class. You are responsible for picking up your copy if you miss getting it on the day it is distributed. Before requesting the regrade, check the solution key (which will be posted on UNM Learn) and state precisely in your claim which step of your solution seems to have been overlooked by the grader.
Academic Honesty
Each student is expected to maintain the highest standards of honesty and integrity in academic and professional matters. The University reserves the right to take disciplinary action, including dismissal, against any student who is found responsible for academic dishonesty. Any student who has been judged to have engaged in academic dishonesty in course work may receive a reduced or failing grade for the work in question and/or for the course. Academic dishonesty includes, but is not limited to, dishonesty on quizzes, tests or assignments; claiming credit for work not done or done by others; hindering the academic work of other students.
No Make-up Policy
No late homework will be accepted. A student is allowed to submit homework by email in a SINGLE PDF file.
American Disabilities Act
In accordance with University Policy 2310 and the American Disabilities Act (ADA), academic accommodations may be made for any student who notifies the instructor of the need for an accommodation. It is imperative that you take the initiative to bring such needs to the instructor's attention, as the instructor is not legally permitted to inquire. Students who may require assistance in emergency evacuations should contact the instructor as to the most appropriate procedures to follow. Contact Accessibility Services at 505-661-4692 for additional information.
It is your responsibility to know and understand the policies discussed in this syllabus. The instructor reserves the right to change this syllabus.