this post was submitted on 20 Jun 2025
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can someone explain me like I'm 5, why is matrix math useful for anything?
Let's say I'm writing a computer game, which features a robot holding a gun. I have a list of vectors representing the 3D model of the gun, but how do I know where to draw those points on screen? To transform the gun model to screen coordinates I just need to do this simple process:
Oh dear, that wasn't so simple. Are we going to do this for every vector in the gun model? Well, as it turns out, the first 10 steps are all linear transformations that can be represented by a matrix. And we can encapsulate the entire process by multiplying those matrices together, so instead of 10 operations, we can combine it into one, a single matrix which will take us all the way from the gun model to a position in camera space. So we just need to pass the graphics card some instructions to tell it what to do, plus the list of vectors for the gun model, plus the combined matrix for transforming them.
There's many other cool things to do with matrices in graphics programming but that's a starting point.
great explanation, thanks
You're welcome, it was a very valid question
You know how you can write "5+5+5-4-4-4" as "35-34", and then use it for weird shortcuts like "3*(5-4)"? Well, matrices make for relatively easy handling of certain systems of equations, letting you fiddle with the whole system at once instead of restating equations one by one.
so it's basically like parallelizing algebra?
Essentially.
A straightforward example would be an equation system: 2x+4y=10, 3x+5y=13. You could solve it manually, or you could call Cramer's rule and plug the numbers into the formula:
Ax+By=C
Dx+Ey=F
x=[CB/FE]/[AB/DE] = (CE-BF)/(AE-BD)=(10*5-4*13) / (2*5 - 3*4) = (50-52)/(10-12)=1,
y=[AC/DF]/[AB/DE]=AF-CD / AE-BD = -4/-2=2
Pure algo, no thinking required. Also note that you don't strictly need x to get y and vice versa.
In a more complex example: You're making a program to draw something in 2D. You could implement mirroring, rotation, scaling etc..., or, you could declare each point (xy) a vector V=[X Y], implement matrices, and then V times [1 0/0 1] gives you V, [-1 0/0 1] gives you V mirrored on the Y axis, [1 0/0 -1] mirrors on the X axis, [j 0/0 j] scales it by j, [cosw -sinw/sinw cosw] rotates it by w... Makes life much easier.
that's a good parallel. as for more uses, a graphics card is basically a big parallel math coprocessor for matrices. so CFD? matrices. call of duty? matrices. all this "ai" stuff nowadays? matrices.
https://kids.kiddle.co/Finite_element_method
Take into account that I have my linear algebra exam in a week and I merely hope to get a passing grade, but apparently, in the very least they are useful for solving systems of equations using very simple algorithm-based operations.