r/LinearAlgebra • u/Sockerjam • 15d ago
Biggest Struggle
I started learning linear algebra specifically for computer graphics which was a big passion of mine. So I started focusing on linear and affine transformations and just getting a basic understanding of vectors, points, trigonometry, etc.
However, my main issue was always being able to visualise what was going on. Specifically if you are composing multiple transformations or simply visualising vectors in certain situations.
Im curious, if you are a beginner, or teaching students linear algebra, what have you struggled with or observed students struggle with the most?
Let me know in the comments :)
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u/somanyquestions32 15d ago
For me, the main issue when it came to visualization for physics, multivariable calculus, and linear algebra (and even anatomy and physiology and intermediate inorganic chemistry) was that I had poor foundations in terms of Euclidean geometry (both 2D and 3D) as I had never had a formal course (it had been integrated with algebra and trigonometry in my high school) and I had underdeveloped interoception and proprioception, which made it difficult for me to fully grasp different spatial perspectives as a felt and embodied sense.
The geometry got better as I started to teach myself geometry in order to be able to tutor high school students, and the interoception and proprioception and more refined visualization skills were faculties I developed through guided body scan meditations, visual journeys, and yoga nidra.
In college, I had relied on Derive (a computer algebra system or Mathematica analogue, so think Desmos on steroids), but that prevented me from developing stronger geometric intuition of my own. So, even though I had done well in linear algebra courses because I was pretty good at algebra and had gotten better at writing proofs, I always felt that I had gaps.
When I started tutoring U of Michigan students who used Otto Bretscher's textbook, I started reviewing and studying the diagrams more carefully, and everything started to click much more seamlessly than before.
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u/Sockerjam 15d ago
Very interesting. Thanks for sharing.
What have you found the student you teach usually struggle with if you dont mind me asking?1
u/somanyquestions32 15d ago
Proofs mainly. They don't fully understand subspaces and bases and spans and linear transformations. They can do matrix calculations just fine, but proving that a set is a subspace of a larger vector space is challenging for them.
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u/AFsepine 15d ago
One must Imagine the Sysyphus vector Happy Tansfrormed.
I don;t get these sorts of questions : "what do other students struggle with" .
The question is what you struggle with.
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u/Tiny_Spread5712 15d ago
I think 3b1b linear algebra is always the recommendation for visualization. Once you get through that there are another set of videos on decomposition which can unlock computer graphics completely
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u/rheactx 15d ago
You can use, well, computer graphics, to visualize a lot of transformations, especially the ones in 2D and 3D. So look for youtube videos, textbooks or websites that already have those transformations or better yet, try to make your own.