Looking for a Linear Algebra Project

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I am in an Intro to Linear Algebra class and we can get some extra credit points but working on a project and producing a 10 page paper. I am interested in doing something in scientific computing, if I could find something with a specific application to astronomy I would be pretty excited. I tried to ask the professor to point me in the right direction but he hasn't been much help yet. Since I am such a novice in L.A. I'm not really sure what kind a project of this kind would look like. Does anyone have any advice or resources to look at.

Btw, in class we don't cover many applications of L.A. what parts of Linear Algebra will really help me figure out how to covert a given problem into a system of equations,etc.
 
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Some friends of mine are taking a large project in maths this year that will use linear algebra in face recognition software; given that they're quite familiar with LA by now and it's worth a significant fraction of their degree I'm not sure how easily you could produce something smaller on it, but thought I'd mention the connection.