Exploring Linear Algebra in Physics and Astronomy: A Project Guide

[lubuntu]

Hi,

I am in a Intro Linear Algebra class, I find the subject pretty cool although the book we are using is crap, I am supplementing with Strang's Book and Video Lectures.

Anyways for extra credit we can do a project that involves linear algebra write a 10 page or so paper on it. I am interested in Physics/Astronomy applications and scientific computing but since I am sort of novice in the fields I might have a tough time narrowing down a topic. Could anyone give me some ideas that could help me find a interesting topic to do the project on.

Thanks,

Mark

 

[VeeEight]

It is hard to give a detailed answer without knowing more about the project. However just looking at the wikipedia page for Linear Algebra, there are lots of cool stuff under the 'useful theorems' section that you may want to look into proving or finding interesting consequences. Undergraduate Linear Algebra usually serves as a foundation for upper year Abstract Algebra and Functional Analysis so looking ahead at some of that stuff would probably impress your teacher.

Here are some (very general) topics that I find interesting:
Cayley–Hamilton theorem, Orthogonal matrices and their properties, LU decomposition and it's applications, Banach spaces, Zorn's lemma, etc.

 

[morphism]

How about trying to see what happens to eigenvalue stuff (a.k.a. spectral theory) when you start working with infinite-dimensional vector spaces? The infinite-dimensional setting is important to quantum mechanics.