Linear Algebra: Math 304
Syllabus for Linear Algebra 2, Winter 2024
This class uses geometric interpretations of the inner product and of linear transformations to represents such transformations using their eigenvalues and singular values, to describe orthogonal sets and projections, and to apply the resulting structures. Dynamical systems, least-square problems, quadratic forms, singular value decompositions, and principal component analysis provide the main applications.
The goals for this class are to understand orthogonal sets, and how the representation of a symmetric matrix using an orthonormal basis results in greatly simplified calculations.
Learning outcomes for the class include: calculation of eigenvalues and eigenvectors for real and complex eigenvalues, creating orthonormal sets with a given span, using inner products to calculate projections, using the Gram-Schmidt process, calculating least-squares solutions, calculating the spectral decomposition of a symmetric matrix, deciding the type of a quadratic form, calculating singular values for a matrix, and using singular value decompositions to calculate principal components.
The textbook for this class is Linear Algebra and its applications by David C. Lay and others (Steven R. Lay and Judi J. McDonald) — depending on the edition. Any one of the third, fourth, fifth, or sixth editions will work.
Homework will be assigned in class and due on Tuesdays (of weeks 2, 3, 5, 6, 7, and 9).
Scheduled events:
Tuesday, January 30. First exam.
Monday, February 26. Second exam.
Final exam: Thursday, March 21 at 8:00 a.m.
Instructor: Edoh Y. Amiran
Office hours: Mondays and Tuesdays at 10:00, Thursdays and Fridays at 11:00; and by appointment (email me to schedule).
Office is BH220; Voice over internet: (360) 650–3487; E-mail: edoh@wwu.edu.
Topics:
First week, Jan. 9 to Jan. 12: Goals for the course. Review of bases and eigenvectors and eigenvalues. Sections 4.3, 4.4, 4.5, 5.1, 5.2, and 5.3.
Second week, 1/16 to 1/19: Similar matrices. Complex eigenvalues and standard form. Sections 5.4 and 5.5.
Monday, 1/15 is Martin Luther King Day.
Third week, 1/22 to 1/26: Discrete dynamical systems. The power method. Sections 5.6 and 5.8.
Fourth week, Jan. 29 to Feb. 2: Inner product. Orthogonal sets. Sections 6.1 and 6.2.
First exam on Tuesday, January 30. Emphasis on sections 5.1 to 5.6.
Fifth week, 2/5 to 29: Projections. Gram-Schmidt (and QR). Sections 6.3 and 6.4.
Sixth week, 2/12 to 2/ 16: Least squares. Section 6.5.
Seventh week, 2/20 to 2/23: Linear models in statistics. Section 6.6.
Monday, 2/19 is Presidents’ Day.
Eighth week, Feb. 26 to Mar. 1: Inner product spaces (and weighted least squares). Section 6.7 (and 6.8).
Second exam on Monday, February 26. Emphasis on sections 6.1 to 6.6.
Ninth week, 3/4 to 3/8: Symmetric matrices. Quadratic forms. Eigenvectors and optimization. Sections 7.1, 7.2, and 7.3.
Daylight Saving Time Begins March 10.
Tenth week, 3/11 to 3/15: Singular value decomposition. Principal component analysis. Sections 7.4 and 7.5.
Grades will be based on a score of 100 points: 20 points for homework, 25 points for the first exam, and 30 points each for the second and final exams. The percentage on the worst of the three exams will substitute for the homework percentage, if that results in a higher overall score. Typically, grades will have cut-offs at 90%, 80%, 70%, and 60% for As, Bs, Cs, and Ds (respectively). Plus or minus grades will be chosen to match gaps in students’ cumulative scores.
Suggestions for success.
- Pay particular attention to definitions, being able to supply examples that illustrate their meaning, and being able to state definitions accurately.
- Do the home work as soon as you have read the material — keep up with the skills and techniques as they are being presented.
- Review previous work occasionally. Explain, to yourself or to colleagues, what setting or assumptions are needed to apply each of our theorems.
- Consult with other students, with tutors in the math center, or with the instructor when a concept or process is not clear.
General processes and resources.
Western Washington University is committed to supporting its students. This includes accommodations for spiritual or religious holidays, support for disabilities, support for organized athletic or cultural activities, and a welcoming class atmosphere for all. Students seeking variation in the scheduling of exams or quizzes should contact Edoh as soon as possible to make arrangements. Students who miss a quiz or exam can make alternative arrangements when they provide appropriate justification.
Resources available to students include the Math Center, the Counseling Center, the Health Center, the Wellness Center, LGBTQ+ resources and many other activity and support groups. Click on any of the previous center and resource names for links.
Legal:
The following are links to information on academic honesty and on religious accommodations.