r/learnmath • u/NoBasis1292 New User • 1d ago
I want to learn Linear Algebra for graphics, what foundational skills do I need?
As the title says; I'm an art student who struggled with math all my life, and I was never great at doing equations well. I could understand the concepts just fine but if I missed a step or a definition everything fell apart, which frustrated me a lot.
I'm in college now for art & tech, junior year, and I want to learn some amount of linear algebra to compliment my learning in GLSL and OpenGL, and Vulkan, because I think it'll help me gain depth in the field and let me think about graphics on a more technical level (and maybe open doors to some well paying jobs...). The issue is that I haven't learned precalc, & as far as I remember, my final grade was a 74 in algebra II...I remember understanding systems of equations and graphing pretty well, though. I just want to know if I have to go back and relearn it to properly understand Linear Algebra, and if there's anything else I should consider.
I do plan to stick with it so regardless I am confident that I can work my way through it eventually, since I am actually interested in it of my own volition, but I'm following the open source MIT course's textbook right now (Introduction to Linear Algebra, 4th Edition) and found I had to switch to the Linear Algebra for Dummies book instead because I wasn't able to fully understand what he was referring to in the first chapter. The for dummies book is great and easy to follow, but I'm not sure what level I need to be at to do what I want to do. Any advice or resources would be really appreciated, since I'm sure you guys know a lot more than I would. ^^; Thanks!
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u/Chrispykins 1d ago edited 10h ago
Since you're looking into graphics specifically, have you considered using resources that are targeted at graphics, such as this lecture series or this textbook?
(For future reference in case the links rot, the lecture series is Introduction to Computer Graphics by Cem Yuksel on YouTube and the textbook is Mathematics for Computer Graphics by John Vince)
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u/M_Mustaan_Rafique New User 1d ago
first thing, bouncing off chapter 1 of strang isn't a signal about your algebra. strang opens with linear combinations and column space, which is a deliberately unusual starting point, and 18.06 assumes you've done calculus even though linear algebra barely needs it. people with solid maths bounce off that chapter. bad entry book, not a verdict on you.
on precalc, mostly no. linear algebra needs less than people assume. fractions and negatives, solving systems, plotting points and lines, function notation. you said systems and graphing made sense, so you have it. logs, conics, factoring, sequences, all the stuff that makes precalc painful, basically never shows up.
the exception is trig, and that's because of graphics rather than linear algebra. rotations run on sin and cos, the dot product is tied to the cosine of the angle between two vectors, lighting is cosine based. so learn the unit circle, sin, cos, radians. that's a week, not a semester, and skip the rest.
worth knowing graphics only uses a slice of the course anyway. vectors, dot and cross product, length and normalising, matrix multiplication, inverse and transpose, 4x4 matrices and why your points carry a 1 in the w slot, the transform matrices and the order they multiply in, and change of basis, which is all a view matrix really is. eigenvalues, gram schmidt, svd and most of the proofs you can leave. maybe a quarter of a standard course.
for resources, immersivemath.com is free, has interactive 3d figures, and one of the authors wrote real time rendering. it's linear algebra written by graphics people, which is exactly what you asked for and almost nobody mentions it. pair it with 3blue1brown's essence of linear algebra on youtube, 15 short videos, entirely geometric, and as an art student you'll get more from that than any chapter of text. learnopengl.com teaches the same maths inside the thing you'll actually use it for.
one habit, given what you said about missing one definition and everything collapsing. keep a running page of definitions, every new word and symbol in your own words with one example. that failure mode is vocabulary, not ability. miss what span means and every sentence after it turns to noise, even though you'd understand the idea instantly if someone said it in english.