What Are the Best Linear Algebra Topics for a Physicist?

[loonychune]

I've been working from a book called 'Linear Algebra' by Georgi E. Shilov and while it is nice to take the more hardcore-mathematical approach, I just don't have the time (nor think it necessary) to get what I need from such a book for physics.

So what I've done so far is looked at systems of linear equations (N equations and N unknowns) and Cramer's rules (which is a nice method for such equations).

However, I'm finding it difficult trying to organise some sort of textbook learning for everything... Riley,Hobson, Bence's book seems to cover lots in detail then side-steps the question of solving homogeneous sets of equations and M x N equations by introducing the method of SINGULAR VALUE DECOMPOSITION and Mary Boas is really too brief in covering things like eigenvalues of hermitian and anti-hermitian matrices, and probably actually too brief in her coverage of eigenvectors/values full-stop.

At risk of going on for too long, let me ask: what would be the best topics to cover?

Would the SVD method be pretty much sufficient, since if i cover the entire chapter in RHB's book, i'll get a good look at things like vector subspaces also?

At the end of the day I have to be able to formulate matrices and solve sets of simultaneous equations and could spend far too long in theory and not actually earn that ability! (course whatever extra could be useful for this year's coming course in quantum mechanics but at the same time this project has come out of me wanting to cover things I've skimmed through in the past)

Damian

 

[tbradshaw]

Linear algebra will help you solve problems faster. Knowing how to find eigenvalues is nice when solving PDE's. This will help you out tremendously. Taking determinants of a matrix comes in hand too when finding cross-products of complicated vectors.