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
https://youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFit...
[1] https://www.youtube.com/watch?v=ei6RfbplYZM
What am I missing?
1. Theoretical (as in vector spaces, etc). These mostly are useful in advanced courses in engineering/science, and a lot of their applications involve calculus (e.g. Fourier series, function spaces, etc). So calculus needs to be taught first.
2. Computational. These can be subdivided into applications that involve calculus (e.g. differential equations) and everything else (graphics, etc).
Many of the latter's applications are relatively recent (last few decades). Whereas calculus was needed in virtually all types of engineering and science. So it made sense to teach calculus.
Imagine it's the 1970's. Your in HS. What will you do with all the linear algebra knowledge that won't require calculus? Assume you have no access to computers.
I personally find geometry and algebra more interesting, but it seems to me that derivatives are more fundamental than matrices. But maybe that's just my bias from being educated like that.
At a high school level, you have students who are either engaged and will likely learn both subjects eventually, or students who aren’t as engaged and are just looking to take their “last math class”. In my opinion, it makes more sense to offer a choice or at least focus on the curriculum that keeps students are that age to most engaged.
As someone who has studied both subjects, I’d go with linear algebra 9 times out of 10, the exception being if someone wanted to also study physics.
Also I would add that linear algebra, calculus, and differential equations all go pretty much hand in hand. We could probably stand to teach anyone with an inclination for STEM all of those much sooner.
Possibly not Calculus 2, but at least getting an intuitive understanding of rates of change, second derivatives, and area under a curve seems pretty critical for all the sciences.
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...
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!
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.
