Linear Algebra Applications in Astrophysics

[Chelsea S]

1.Well this isn't a specific homework problem, I just need a quick idea to use for a paper.
Our linear algebra professor is giving us a 50 point paper project/report that has to do with the applications of linear algebra in the field of study we have chosen to pursue. I would like to do astrophysics but have not gotten high enough in physics, much less specific enough into astrophysics to know what the applications are of linear algebra in the field.

Specifically, it SHOULD be something that we have already gone over in class; it's just been a pretty basic introductory class, ranging from basic matrix arithmetic, to change of bases, transformations, null/kernal/column space and eigenspace/values/vectors. It can be something we have not covered in class, but I have to prove my 'mastery' of it in the paper.

If someone knows an application for it, and could briefly describe it or point me in the right direction to a web page that describes it that would be so very helpful.2. Homework Equations : That's what I'm here for
3. I have already asked Uncle Google but he hasn't given me anything useful, so here I am in a specific community that may already know.

 

[collinsmark]

Hello Chelsea S,

Since nobody has responded yet, maybe I'll try to give it a shot.

Linear algebra is all over the place in astrophysics. So there's no shortage there. I'm just trying to think of a specific area that's not too advanced.

The Einstein field equations contain 16 simultaneous differential equations (10 of them independent). But this subject involves things such as tensors, generalized coordinates, and not to mention the fact that they are "differential" equations. So I think this is too complicated for your purposes, and I don't recommend it.

Quantum mechanics deals with linear algebra all the time, particularly when two or more particles are involved (google "S-matrix"). And quantum mechanics applies to astrophysics, particularly in the field of high-energy physics. Linear algebra is necessary when transforming one Hilbert space into another (again, particularly when more than one particle is involved). There are more eigenvalues and eigenvectors than you can shake a stick at. But this is really, really complicated, and once again it mostly deals with "differential" equations, so I don't recommend this either.

You might want to touch on the Lorentz transformation in special relativity. Anything involving relativity has some application in astrophysics. (Google "Lorentz transformation.") It's not simple by any means, but it might be do-able.

 

[Chelsea S]

Hey Thanks for the reply!
It gets me pointed in the right direction, at least.
I can't believe I never even though to pick up my Q.M book... because Astrophysics has nothing to do with things moving the speed of light *sarcasm*

Thanks for the help! I appreciate it!

 

[tms]

For something a little easier, you might look at transforming between geocentric and heliocentric coordinate systems. This is useful in determining orbits of comets or asteroids or whatever in orbit around the Sun, since all observations are made from Earth.

Some linear algebra is also used in Gauss's method of orbit determination.

 

[Chelsea S]

Oh neat! Thanks!