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.
Schedule
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
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.
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It is your responsibility to know and understand the policies discussed in this syllabus.
The instructor reserves the right to change this syllabus.