Application of Linear Algebra to Physics

[azupol]

I've just begun my 2nd year of study at my University and as part of a program requirement, must take a Liner Algebra course. I love mathematics, but I have never experienced much of Linear Algebra. I was just wondering how Linear Algebra applies to Physics, what branches, etc.

 

[TheFerruccio]

The first thing that came to mind for me was the use of Hilbert spaces in quantum mechanics.

Linear algebra also has applications in designing feedback control systems, dealing with something called "state space."

I extensively used linear algebra when dealing in aerospace structures classes, representing stresses and strains as a matrix.

This PDF might explain a bit in more detail:

http://www.math.uni-bielefeld.de/~hemion/Linear_Algebra_in_Physics/LinearAlg.Physics.pdf

It's pervasive and entirely necessary. You'll be using it all the time, and it makes a bunch of mathematics a whole lot easier.

 

[HallsofIvy]

I would take the "Hilbert spaces in Quantum mechanics" with a grain of salt. "Linear Algebra", strictly speaking, deals with finite dimensional vector spaces while Hilbert spaces are infinite dimensional- the domain of "functional analysis". Of course, one had better have a good grounding in Linear Algebra before starting "functional analysis".

 

[azupol]

Thanks for your responses and the PDF, it was very helpful and descriptive. I suppose my next question would be, what would be some math courses you guys would recommend I take to further my understanding of Physics? Along with Linear Algebra, I am also taking Multivariable Calculus, Differential Equations, Concepts in Abstract Mathematics, and Complex Analysis.