Math 316 syllabus
Linear Algebra II
Course Description: A continuation of MA 237. Topics include inner product spaces, spectral theorem for symmetric operators, complex vector spaces, Jordan canonical form. Additional topics such as duality and Tensor products among others to be included at the discretion of the instructor.
Prerequisites: C or better in MA 237.
Suggested Text: A Course in Linear Algebra, by David B. Damiano and John B. Little, Dover Publications,
Coverage: Chapters 4 through 7.
Learning outcomes: Upon the successful completion of the course a student will:
- Develop a good conceptual and computational understanding of linear algebra.
- State definitions precisely, prove some small theorems, follow the proofs of bigger theorems, and apply the aforementioned in a variety of real world situations.
- Learn about diagonalizability, the spectral theorem, and the Jordan canonical form.
- Learn about the matrix exponential and how to solve systems of linear differential equations with constant coefficients.
- Learn about the singular value decomposition and its applications such as lossy compression.
- Be introduced to a selection of additional applications of linear algebra such as (multiple) linear regression, Markov chains, connections to graph theory and Fourier series.