Advanced Linear Algebra
Arizona State University, Fall 2024
Instructor: Zilin Jiang ([email protected])
Please reserve email only for individual, non-technical matters; use the office hours for technical questions related to lectures and assignments.
Office hours: Tuesdays and Thursdays 1:30pm - 2:30pm in WXLR 839.
Course description
This course offers a unique approach by emphasizing abstract vector spaces and linear maps over the traditional focus on Euclidean spaces and matrices, particularly through determinant-free proofs for the existence of eigenvalues on complex vector spaces.
Key concepts include the definition and basic properties of vector spaces, linear independence, basis, dimension, linear maps and their fundamental theorem, the theory of polynomials in relation to linear operators, eigenvectors, inner product spaces, the spectral theorem, and advanced topics such as the generalized eigenspace decomposition and Jordan form.
This course diverges from the norm by postponing the introduction of determinants to the end, facilitating a deeper understanding of linear operators and their structures without the initial complexity of determinants. Through this restructuring, students gain insights into the connections between different mathematical areas and are better equipped to handle exercises that demand a strong understanding of proofs.
Enrollment requirements
Prerequisites: No prerequisites other than the usual demand for suitable mathematical maturity.
Grade policies
A+ ≥ 97%; A ≥ 94%; A- ≥ 90%;
B+ ≥ 87%; B ≥ 84%; B- ≥ 80%;
C+ ≥ 76%; C ≥ 70%; D- ≥ 60%; E otherwise.
Absence policies
In general, no late submission of assignments will be accepted unless there is a genuine emergency backed up by official documents (such as a physician's note attesting the same).
Textbook
Primary references: Sheldon Axler, Linear algebra done right. Fourth edition. Springer, 2024. Open access: https://linear.axler.net/
Assessment and Assignments
- Homework: 30% — There will be weekly assignments. Late submission of homework will not be accepted. No grade appeal will be considered after one week of the posting of the grade for any assignment.
- Two midterms: 40% — September 24 and October 31, 2024. No make-up test will be given unless a student has notified the instructor before the test is given.
- Final: 30% — December 10, 2024, 12:10pm–2:00pm