Today was a whole lot of math! Specifically, linear algebra. Actually, not that much, since I took an introduction to linear algebra last year, but as we all know, math instruction rarely sticks. At least for me it didn’t. A complaint I had a lot last year, and which I want to try and fix this second time around, is that things just felt so unintuitive. I didn’t understand the intuitions behind all these multiplications and factorizations and spaces I was learning about, much less how to apply them to more complex scenarios (such as ML) so I’m really trying to focus on geometrical representations and understanding it thoroughly!
I’ll admit it is difficult to really internalize these highly abstract (to me) concepts. Of course, 3Blue1Brown’s videos are massively helpful, and glad to see his beautiful, familiar animations. But I also know his videos don’t suffice for the level of understanding that I’m going for, so I’m following along with two textbooks I heard were decent: Gilbert Strang’s Linear Algebra and Its Applications, and Sheldon Axler’s Linear Algebra Done Right. Just from skimming a couple of pages, I can definitely already tell that the styles are very different between the two, so I’m going to try to cross-check and read both simultaneously.
As for the textbooks, my progress wasn’t huge. I read through the Vector Spaces chapter in Axler’s textbook, many of the topics of which were surprisingly familiar! I reunited with my beloved ring axioms and rudimentariest of the rudimentary proofs that I encountered at Ross, which was a lovely (?) callback. But this has actually also been the first time I’ve seen these concepts “in the wild” which I guess goes to show just how in-depth this textbook goes. Some of the notation is foreign to me, and I don’t quite like the way some things are explained and proven (or that might just be the order he chooses to introduce topics in), but I think it’s pretty well-written overall.
Tomorrow I plan to go over the same chapter, Vector Spaces, in Strang’s textbook. I’m a little nervous because it seemed kind of difficult to read earlier when I skimmed it (and it’s the second chapter) but it should be fine. I look forward to finally actually understanding what the null space and column space are, and to hopefully put some intuition to that with the next 3B1B video!
I also want to try to learn the programming parts/fundamentals along with the math. I don’t know how well that syncs up, or if at all, besides basic numpy arrays, but we’ll see if I can integrate some of the math into the coding… because let’s be honest I also need to brush up on that. Overall, I’m excited about starting this journey, since I really think it’ll be valuable for me in the future. It’s a topic (as evidenced by this post) that sits squarely at the intersection of math and computer science, which are two things I’m genuinely really interested in, and I look forward to seeing how this plays out!