# Advanced Linear Algebra

This page contains a list of ideas for DRP projects, but is by no means exhaustive.

**Topic:** Finite Dimensional [latex]C^*[/latex]-Algebras

**Suggested Background: **MATH 2600 (Linear Algebra)

**Topic:** Quantum Mechanics

**Suggested Background: **MATH 2600 (Linear Algebra)

**Description: **When people think of physics, they often think of physical phenomena at the macroscopic scale (the momentum of a wrecking ball or the velocity of a car for instance). However, the theories of classical physics don’t work when trying to capture the behavior of things at the atomic scale. Quantum mechanics was developed to fill this hole in our understanding! The main mathematical tool to model quantum mechanical systems are Complex Hilbert Spaces (see above). This project would focus on exploring the connection between Hilbert spaces and Quantum mechanics.

**Topic:** Markov Processes

**Suggested Background: **MATH 2600 (Linear Algebra)

**Description: **A Markov process is a stochastic process that can make predictions using only the current state of a system (importantly — the past plays no role in the prediction). As it turns out, these processes are very useful when it comes to modeling real world phenomena as well as being heavily used in various data analysis/machine learning algorithms.

**Topic:** Perron-Frobenius Theory

**Suggested Background: **MATH 2600 (Linear Algebra)