MA 471: Linear Algebra 2
Kurt Bryan, Spring 2015-16
What is this course about?
This course builds on Linear Algebra 1 (duh!) to go a bit deeper into certain topics, e.g., eigenvalues and
the singular value decomposition, and other classic matrix factorizations, though we'll explore many additional topics and modern applications
of linear algebra. Some potential applications are
- The application of the singular value decomposition (SVD) to compression.
- The application of the SVD to linear least squares problems and inverse problems.
- Principal Components Analysis, an important topic in mathematics and statistics, widely used in industry.
- The use of eigenvectors and the Perron-Frobenius Theorem to search engines (e.g., Google) and Markov methods.
- The "matrix completion" problem, with applications to estimating user preferences (e.g., how does Amazon target ads to you? How does Netflix decide what movies to recommend to you?)
- Compressed Sensing, a red-hot new area of applied math/stats/computer science/electrical engineering. It allows one to solve certain problems
when it looks like there's not enough information to find a solution. Researchers have used these ideas to build a "one pixel" camera! We'll look at applications to signal
analysis, image processing, machine learning, who knows?
Course Structure
The course work will consist of homework assignments (about one per week) and a couple of take home exams.
The prerequisite is Linear Algebra 1 (MA 371) or Applied LInear Algebra (MA 373).
On the left below is an illustration of the "single pixel camera." On the right is an original image and image captured with the single pixel camera.
Check out
Wikipedia's page on Compressed Sensing.