Self Studying Proof-Based LinAlg

[Dark Avorian]

Hey guys, so for various reasons I'm trying to self study some mathy type stuff. I want to do some linear algebra, but everything I've found online seems fairly concrete, and while I know I'm going to have to do rote work to get the hang of it all, I'd really love a resource that also helped me work on my proof skills fairly rigorously at the same time. I'd prefer it if it was accessible online, and free. Thanks for any suggestions.

[gfauxpas]

Try these:

http://www.khanacademy.org/#linear-algebra - math videos, most by educator Sal Khan, my favorite math resource.
http://www.proofwiki.org/wiki/Category:Linear_Algebra - math wiki. You can find theorems that aren't up yet and prove them, for practice.
http://tutorial.math.lamar.edu/Classes/ ... inAlg.aspx - lecture notes from a college math professor "Paul", pretty good stuff but may not be proofy enough for what you're looking for.

[Tirian]

I love me some Salman Khan, but his presentation is entirely concrete. And I totally support the plan of learning linear from an proof-based foundation. Linear Algebra can be so much more than arithmetic in R^k, but I'm afraid that too many people miss that opportunity from overly "practical" introductions.

A little Google-fu led me to Sergei Treil's Linear Algebra Done Wrong, which from a brief scan strikes me as a pretty sweet book. There are some proofs in the homework sections, but what you really want to get into the habit of doing when reading textbooks is to see every proposition in the text as an exercise that is immediate followed by its solution.

[Dark Avorian]

So maybe a bit more context would be helpful. I've gone through most of Strang's lectures on MIT OCW, so I'm pretty firm on understanding what the basic building blocks of the linear algebra vocabulary are, and the most basic definitions. I've worked through, in a bit of depth, Spivak's Calculus and Gallian's Contemporary Abstract Algebra so I have something of a handle on how proof works. I just need a programmatic way to look through Linear Algebra's major theorems, and then hopefully problems that apply them in a theoretical way.

[gorcee]

"Hi, I'm the Sheldon Axler book, Linear Algebra Done Right. I'm the biggest piece of shit you'll ever buy. First, I'm going to use a super-condescending tone throughout the book. Just my name is super pretentious. Wait, hold on, let me explain what a number is to you. Got that? Good, because I'm going to be explaining all sorts of simple concepts. Don't get used to explanations though, because when it comes to more advanced concepts, you're own your own. Hah!

It occurs to me that sometimes, students learning a new topic might like to see examples. So, here's an example: Problem statement. Solution: left as an exercise for the reader. HAHA! See, that's an example of how I'm going to fuck you over for the next 90 pages. I'm going to tell you that you don't need an abstract algebra background to understand this material, then, three pages later, I'm totally going to expect you to have an abstract algebra background. BUT I'M DOING IT RIGHT BECAUSE I SAY SO."

Seriously, avoid this book at all costs. There are far better introductions to mathematically rigorous linear algebra. Even some that merge the practical with the theoretical.

[Dark Avorian]

Incredibly helpful. Thanks.

[gorcee]

Incredibly helpful. Thanks.

Sorry. I had to dig the book out the other day, and the "Linear Algebra Done Wrong" title reminded me of this rage.

Incidentally, there's a reason why "Linear Algebra Done Wrong" was titled so.

If you have access to a university library, Strang's book does a decent job at tying in the theoretical concepts to the practical ones, which helps you understand the theoretical concepts if you already have a grasp on the practical ones.