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The Art of Linear Algebra [pdf]

by allending on 9/30/21, 8:11 AM with 42 comments

• by ivan_ah on 9/30/21, 10:37 AM

  Wow this is really well done. It's like a visual-algebraic approach... I've never seen this before.

  I like how the author sets up a "grammar of matrix multiplications," and then reuses the same patterns in the rest of the document.

  For people who might not be familiar, these visual notes are inspired by and complement Prof. Strang's new book https://math.mit.edu/~gs/everyone/ and course https://ocw.mit.edu/resources/res-18-010-a-2020-vision-of-li... https://www.youtube.com/playlist?list=PLUl4u3cNGP61iQEFiWLE2... see also https://news.ycombinator.com/item?id=23157827

• by jasode on 9/30/21, 9:26 AM

  It seems like the "github.com" link would be a better and more canonical url rather than link an opaque url to "githubusercontent.com"

  https://github.com/kenjihiranabe/The-Art-of-Linear-Algebra

• by antegamisou on 9/30/21, 12:15 PM

  Also check out 3Blue1Brown's Essence of Linear Algebra

  https://youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFit...

• by ChicagoBoy11 on 9/30/21, 6:34 PM

  I never understood why we don't do more of this stuff in school, and how calculus instead became the defacto advanced math curriculum in most high-schools. Students grow up working on their basic algebraic operations, solving equations, etc. Liner Algebra introduces them to the universe that lies just beyond those techniques, has very readily applicable uses, lends itself excellently to simulation/connections to computer science (which is super popular to teach now), etc.

• by hiranabe on 10/1/21, 6:08 AM

  Hello, I'm the author of the article, thanks for the nice comments.

  This article should have been titled as "Graphic Notes on Linear Algebra for Everyone", and Prof. Strang kindly suggested this big name. I was lucky that this drew this attention.

  There are some other visuals I'm trying around the area. - Eigenvalues https://anagileway.com/2021/10/01/map-of-eigenvalues/

  -Matrix classification https://anagileway.com/2020/09/29/matrix-world-in-linear-alg...

  When I was an undergraduate, I didn't get this understanding of linear algebra... but after watching all the Prof. Strang's 18.06 classes in MIT OpenCourseWare, now I have much clear view of this area... So I really appreciate his way of teaching.

  BTW, I even made a T-shirt and sent him ! https://anagileway.com/2020/06/04/prof-gilbert-strang-linear...

• by skytreader on 9/30/21, 10:52 AM

  Instantly fell in love with the presentation! Might give this a read-through just out of pure curiosity.

  In undergrad, my mnemonic for these operations was visualizing the matrices animated in my head. The more complex ones, it was actually easier for me to remember Scheme functions that represent the algorithm (all expressed via higher-order functions so it was pretty concise); this was unique to my circumstances as an undergrad, not something I can pull off today without reviewing a lot of material.

  Presenting the operations with color and blocks just gives a more natural "user interface" (lacking a better term) for remembering it!

• by amelius on 9/30/21, 10:56 AM

  On the first page they say "if neither a or b are 0", but they haven't defined what it means for a vector to be 0.

  Also, they say "rank 1 matrix", but they haven't defined the concept of rank yet.

  Some readers might find this kind of presentation acceptable, but personally I strongly dislike it when concepts are used before they are defined.

• by visarga on 9/30/21, 9:47 AM

  Nice, I was just reviewing SVD and PCA, I grok them but then I forget, this material is useful for remembering the big picture.

• by hwers on 9/30/21, 12:16 PM

  I keep seeing the same material like this (and love it btw) but I keep thinking that it's all only scratching the surface. From what I've seen in abstract algebra this stuff goes way deeper and becomes way more beautiful. I would love the "homemade" explanations and visualizations to start enlightening us about that. E.g. so DIY machine learning folks like the amazing GAN art community that's cropping could get more tooling to pluck easy hanging fruit.

• by jnurmine on 9/30/21, 9:14 PM

  Would love to see other things like physics, chemistry, etc. done with this kind of representation. Visualized, concise descriptions.

• by _wldu on 9/30/21, 11:18 AM

  This is great for those studying algorithms (DP, DC, FFT, etc.). Very useful.

• by Matt-Gleich on 9/30/21, 7:09 PM

  Great visuals

• by tishha on 9/30/21, 12:11 PM

  good notes, very useful!