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Comment by chongli | Hacker News Reader

I don’t want to study math in the traditional way, with convoluted abstract examples that lead nowhere

Have you checked out Gilbert Strang's lectures [1]? They're definitely geared toward numerical/applied linear algebra rather than theoretical/abstract.

[1] https://www.youtube.com/watch?v=7UJ4CFRGd-U&list=PLE7DDD9101...

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I watched it, still either too abstract or too much doing math for the sake of math, not enough explaining why I would want to take the inverse of a determinants eigenvalue or whatever the fuck linear algebra is supposed to be about, because halfway through the course I still had barely a clue what the point was.

Maybe you would get something out of 3blue1brown's series on linear algebra [1]. It will give you an intuitive, geometric interpretation for concepts such as a vector, a basis, an eigenvalue, a linear transformation, etc.

As for why you would want to know these things, well, linear algebra is finding applications all over the place these days. Everything from computer graphics to machine learning is jam-packed with linear algebra. And I'm not just talking about basic concepts such as matrix-vector multiplication. The singular value decomposition has applications in discrete optimization, image compression, the PageRank algorithm [2], computer vision [3], and machine learning [2] [4].

Having said that, you may find it very difficult to understand something like SVD without a firm grounding in the topic of vector spaces, linear transformations, spanning, linear (in)dependence, subspaces, eigenvalues, eigenvectors, diagonalization, and determinants. This is why SVD is one of the last things you learn in a linear algebra course (indeed, it's not covered until lecture 29 of Gilbert Strang's course).

Ultimately, it all depends on how relevant these things are to you. I would assume (hope) that because you clicked on this HN discussion that you're interested in learning linear algebra because you think it might be useful to you.

[1] https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQ...

[2] http://www.cs.cornell.edu/courses/cs4850/2010sp/Course%20Not...

[3] http://cs.rkmvu.ac.in/~sghosh/public_html/nitw_igga/talk.pdf

[4] https://medium.com/@jonathan_hui/machine-learning-singular-v...

I agree on your assessment of Gilbert Strang's courses. So many here on HN recommend Strang's stuff. However, he's kind of the victim of his own success. If you've taken LA in college in the last 10-15 years, or any online LA class like Khan Academy, they teach from a geometric approach like he advocates and pioneered. Therefore, you're not exactly learning anything new, just a different person saying it; which, of course, might help. But it's still LA for the sake of LA.

Mind you, they are very good, and out of all online courses I've seen, the questions are actually hard and make you think and understand on a deeper level. Every other course I've seen have simple, fluff questions, if any.

Tim Chartier of Davidson College put out a class on EdX called Applications of Linear Algebra. It's more practical, but I found Part 1 to be too practical and not enough math. It suffers from the opposite problem. Part 2 may be better, but I didn't make it through. Plus, I found his style to be a little woo-woo. You might have some success with it because he actually does talk about real world scenarios.

https://www.edx.org/course/applications-of-linear-algebra-pa...

I've actually looked at about half a dozen online LA resources that take different approaches. I should do a blog post about them one day.

Yes, please do a blog post comparing the different approaches to teaching LA.

Are there many different styles for teaching Linear Algebra, though?

I'd definitely be interested in seeing how different resources teach it.

LA pops up in many places. For me, I've tried reading enough books and papers over time which assumed I knew what a basis or a singular matrix or SVD is that I decided to just jump in and learn this stuff. I went through Strang (took me perhaps 100-200 hours of study) and I'm very glad I did it.

But that course is the very basics that you need before you can start doing applications. Just like you have to learn a bit of vocab and grammar before you can start conversing in a foreign language. Once you’ve done that course you could start to actually learn some AI or optimisation or whatever.

If you want, there is a course called 18.065 that he is written that is about AI and is far more application-based. He reviews the 30 hours or so (by lecture time) of his famous LA course in the first 5 or so lectures before springing off into everything you need to end up with AI.

But the contents of his classic course (having an intuition for the 4 subspaces, describing and decomposing matrices in terms of the eigenvalues and vectors, analogies for non-square matrices) are in no way maths for the sake of maths, they are fundamental to understanding any onward applications of LA. They are the very basic words and grammar that let you start using LA in real combat situations. So that you could pick any random paper on ai or stats or control theory and actually be able to follow it rather than just be staring at hieroglyphics. It’s really worth the 30 or so hours of your life.

Well in the end it's still LA you're watching. Linear Algebra is the study of those linear systems, the determinants, the eigenvalues etc. How they behave and why. The abstractness is the "nature" of the LA approach and a bit of mathematical curiosity is needed.

If that's not what you're looking for than maybe you won't be satisfied with any variant of an LA introduction. There's probably a lecture somewhere which teaches the math in combination with an application.

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