How to prepare...

[hotcommodity]

So I'll be taking Linear Algebra come January, and I always like to be prepared or at least a little familiar with material I'm about to encounter. About linear algebra, I have no clue...I know it deals with matrices, at that's it, plus I'm a little rusty on those as I haven't worked any since high school. Can anyone give me a heads up on some of the general ideas of the course, what to look out for, or maybe even a recomended book?...ty

[Klaynos]

matricies, eigenvalue equations, and I *think* intergration, line intergrams, stokes theorem...

[ajb]

Linear algebra = vector spaces and their operators.

[EvoN1020v]

I'm currently taking Linear Algebra in University, and you won't need to panic on the first day. They will introduce you to the concept of a "vector". Then you will go on to vector addition, scalar multiplication, vector subraction.

 

I recommend the "Linear Algebra: A modern introduction, 2nd edition by David Poole", if you want to get familiar with the materials.

 

To let you know, the class is not really that hard, so you should be fine.

[hotcommodity]

Cool Well thanks for the responses, and thanks to Evo for the book recomendation, I'll try and track it down.

[EvoN1020v]

hotcommodity, if you have any further questions about linear algebra, please don't hesitate.

[woelen]

It depends on what you precisely understand with the term "linear algebra". I have had a series of 3 courses on the subject.

 

The first was about vectors and matrixes. Addition, multiplication, non-square matrixes, systems of linear equations, orthogonal spaces, rank of matrixes, null-space of matrixes. Easy stuff...

 

The second course was on linear operators, eigenvalues and eigenvectors. Different norms on a space, special cases: 1-norm, 2-norm (normal euclidian norm for vectors), inf-norm. Norms on matrixes, which are somewhat more complicated for 2-norms (requires eigenvalues of products of matrixes).

Things, also covered in the second course, were numerical computation of eigenvalues, how hard this is, and the problem of computing eigenvectors. Decomposition of matrixes in several forms, singular value decomposition, etc.

 

The final course was on infinite-dimensional spaces. Hilbert spaces. Representation of functions, norms of functions, approximations of functions. Inner products on general vector spaces, orthogonality. Partial differential equations, and how these can be solved in terms of eigenvalues of linear operators on infinite dimensional vector spaces.

 

 

The last course was very abstract and by no means was easy stuff (at least not for me), but it was a pre-requisite for physics courses on quantum-mechanics and subsequent courses on the workings of semiconductor devices. The first two courses were quite easy for me and I did not have any trouble going through them.

 

As you can see, the field of linear algebra is a very wide one. And after my third course, there undoubtedly is much more to tell about the subject, it is a very large field of mathematics.

[ajb]

I would call a course on Hilbert spaces "functional analysis". It is the infinite dimensional version of vector spaces and operators. It is fundamental in quantum physics.