Learning Matrix Mechanics (and other Appl. of Linear Algebra)

[ModestyKing]

So, I'm interested in using my knowledge of elementary linear algebra (I can do projections, rotations, diagonalization, find eigenvalues/states/vectors, and a couple of other things) to learn other things based off of it.

Is there an 'advanced linear algebra' sort of class? My institution offers Numerical Linear Algebra, and Linear Optimization (seems to be along that route), but I'm not sure what other classes (particularly in Physics, Mechanical Engineering, Mathematics and Computer Science) are heavy on usage and learning of linear algebra. I think it's a great concept that can be applied a lot more than it has.

For example, I'd love to take a class about this: http://en.wikipedia.org/wiki/Matrix_mechanics#Development_of_matrix_mechanics

For easy reference in case you guys know more about it than me and are willing to help, here's the undergrad bulletin (includes names and basic descriptions of classes), and the class descriptions start on page 181 or so. The departments are in alphabetical order. http://www.iit.edu/ugaa/pdfs/undergraduate_bulletin_2012_2014-v2.pdf

Some of the syllabi of the classes I can find, but not all, which is why I'm asking for your guys' help. :) This is for my learning's sake.

 

[jasonRF]

What is your major? Many courses that apply linear algebra will have prerequisites besides just linear algebra, so knowing your major and interests can really matter. For example, as an electrical engineering major I took a few classes that really used linear algebra, but you had to take several of the required EE courses to be properly prepared for them.
jason

 

[ModestyKing]

Hi there and thanks for the response,
I'm an Applied Physics major (at my university, it's a mix mix between the physics and mechanical engineering degree). I mentioned I'm interested in Physics, Computer Science, Mechanical / Aerospace Engineering, and Mathematics courses that build upon linear algebra. For example, I know Statics classes in Engineering can use it heavily, right?
Maybe there's even a text focusing simply on Linear Algebra's applications to different sciences and disciples, with preassumed knowledge of the concepts - that would be very cool.
Thanks,
Adam

 

[Gauss M.D.]

The classes it's been most heavily used for me has been in optimization, control theory and advanced statistics (google for 'principal component analysis') so far. But meh, you'll get more matrices and vectors than you could shake a stick at as soon as you start tackling real world problems - meaning those that are too complicated to handle analytically. For your particular discipline, there's probably upper level courses dealing with dynamics, robotics and control systems which can be very computer intensive. Any numerical analysis course, or anything with the words "modeling" or "simulation" would probably be good aswell.

 

[ModestyKing]

Hi there Gauss,
Thanks for your input!
There are various computational courses (Computational Physics, 4th year class, Computational Mechanics/Mathematics (same class, diff. dept), 3rd year class, a few others), as well as numerical PDEs, and also classes in 'mathematical modeling', two semesters of it, each a 4th year class.

I'm excited to learn more and really dig into stuff using matrices and vectors as tools to tackle real world problems, esp. matrices, as I think they're a great tool.