Where to start learning Linear Algebra?

You are right: Linear Algebra is not just the "best" place to start. It's THE place to start.

Among all the books cited in Wikipedia - Linear Algebra, I would recommend:

• Strang, Gilbert, Linear Algebra and Its Applications (4th ed.)

Strang's book has at least two reasons for being recomended. First, it's extremely easy and short. Second, it's the book they use at MIT for the extremely good video Linear Algebra course you'll find in the link of Unreasonable Sin.

For a view towards applications (though maybe not necessarily your applications) and still elementary:

• B. Noble & J.W. Daniel: Applied Linear Algebra, Prentice-Hall, 1977

Linear algebra has two sides: one more "theoretical", the other one more "applied". Strang's book is just elementary, but perhaps "theoretical". Noble-Daniel is definitively "applied". The distinction from the two points of view relies in the emphasis they put on "abstract" vector spaces vs specific ones such as $\mathbb{R}^n$ or $\mathbb{C}^n$, or on matrices vs linear maps.

Maybe because my penchant towards "pure" maths, I must admit that sometimes I find matrices somewhat annoying. They are funny, specific, whereas linear maps can look more "abstract" and "ethereal". But, for instance: I can't stand the proof that the matrix product is associative, whereas the corresponding associativity for the composition of (linear or non linear) maps is true..., well, just because it can't help to be true the first moment you write it down.

Anyway, at a more advanced level in the "theoretical" side you can use:

• Greub, Werner H., Linear Algebra, Graduate Texts in Mathematics (4th ed.), Springer

• Halmos, Paul R., Finite-Dimensional Vector Spaces, Undergraduate Texts in Mathematics, Springer

• Shilov, Georgi E., Linear algebra, Dover Publications

In the "applied" (?) side, a book that I love and you'll appreciate if you want to study, for instance, the exponential of a matrix is Gantmacher.

And, at any time, you'll need to do a lot of exercises. Lipschutz's is second to none in this:

• Lipschutz, Seymour, 3,000 Solved Problems in Linear Algebra, McGraw-Hill

Enjoy! :-)

I'm very surprised noone's yet listed Sheldon Axler's Linear Algebra Done Right - unlike Strang and Lang, which are really great books, Linear Algebra Done Right has a lot of "common sense", and is great for someone who wants to understand what the point of it all is, as it carefully reorders the standard curriculum a bit to help someone understand what it's all about.

With a lot of the standard curriculum, you can get stuck in proofs and eigenvalues and kernels, before you ever appreciate the intuition and applications of what it's all about. This is great if you're a typical pure math type who deals with abstraction easily, but given the asker's description, I don't think that a rigorous pure math course is what he/she's asking for.

For the very practical view, yet also not at all sacrificing depth, I don't think you can do better than Linear Algebra Done Right - and if you are thirsty for more, after you've tried it, Lang and Strang are both great texts.

MIT has a complete online course for linear algebra, complete with video lectures, lecture notes, and assignments.

http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2005/

I'm not sure how much of the course is applicable to what you'll be doing in game development, but it's a solid foundation.