4 ms·

`ridiculously` might be hyperbole, but the two biggest ones I can think of are computer graphics and machine learning; these of which you can't even sneeze at w

by platz 13y ago

`ridiculously` might be hyperbole, but the two biggest ones I can think of are computer graphics and machine learning; these of which you can't even sneeze at without getting in linear algebra.

tptacek 13y ago
I have some sense of the linear algebra implicated in machine learning (I lived for many years with a comp. neuroscience PhD), but I have no visibility into graphics. So with my ignorance pinned to my lapel: the linear algebra involved in computer graphics is pretty simple, right? Just knowing how to manipulate vectors and matrices? Not a lot of eigenvalues, or for that matter orthogonalization? I'm asking not to rebut but because I hope to prompt the sort of "sell us on linear algebra" statement that will make me study harder. :)
- platz 13y ago
  Disclaimer: I'm not very experienced with CG, but I think your intuition is correct on CG, for lots of 'boilerplate' game or photoshop programming. However, I do think you can find plenty of examples in academia. For example, applying PCA http://cmp.felk.cvut.cz/~hlavac/TeachPresEn/11ImageProc/15PCA.pdf http://cmp.felk.cvut.cz/~hlavac/TeachPresEn/11ImageProc/15PC... (Perhaps this is just the result of crossover between CG and ML/Statistics here). Not a good sell, but perhaps someone with more experience can chime in.
- jfarmer 13y ago
  Much of computer graphics operates in projective space (http://en.wikipedia.org/wiki/Projective_space http://en.wikipedia.org/wiki/Projective_space), so it's a little bit more than cookie-cutter linear algebra. This is done so that translations in 3D space — which aren't linear transformations — can be represented as 4D linear transformations in projective space via homogeneous coordinates (http://en.wikipedia.org/wiki/Homogeneous_coordinates http://en.wikipedia.org/wiki/Homogeneous_coordinates). Still, many folks use the APIs without really grokking that, so in practice it can be a bit cookie-cutter. I think of it similarly to how people can use crypto APIs without, say, really understanding what's going on under the hood. BTW, projective space is also intimately related to elliptic curves (as you may or may not know — not implying anything!). So that darn linear algebra is lurking all over the place. Likewise, any time you're talking about fields (even finite fields), vector spaces and linear algebra are right around the corner.
  - tptacek 13y ago
    I'm familiar with projective coordinates for elliptic curves, but the funny thing about curves is that, for high-speed software, the math is tricky enough that you don't "need" to grok it: there's an "explicit formulas database" that you can just copy from: http://www.hyperelliptic.org/EFD/g1p/index.html http://www.hyperelliptic.org/EFD/g1p/index.html Curves are what made algebra 'click' for me, getting me from my high school understanding of "algebra is math about unknown variables" to "algebra is about sets of related objects with operators that have identities and inverses".

by platz 13y ago

`ridiculously` might be hyperbole, but the two biggest ones I can think of are computer graphics and machine learning; these of which you can't even sneeze at without getting in linear algebra.

tptacek 13y ago

I have some sense of the linear algebra implicated in machine learning (I lived for many years with a comp. neuroscience PhD), but I have no visibility into graphics. So with my ignorance pinned to my lapel: the linear algebra involved in computer graphics is pretty simple, right? Just knowing how to manipulate vectors and matrices? Not a lot of eigenvalues, or for that matter orthogonalization? I'm asking not to rebut but because I hope to prompt the sort of "sell us on linear algebra" statement that will make me study harder. :)

platz 13y ago
Disclaimer: I'm not very experienced with CG, but I think your intuition is correct on CG, for lots of 'boilerplate' game or photoshop programming. However, I do think you can find plenty of examples in academia. For example, applying PCA http://cmp.felk.cvut.cz/~hlavac/TeachPresEn/11ImageProc/15PCA.pdf http://cmp.felk.cvut.cz/~hlavac/TeachPresEn/11ImageProc/15PC... (Perhaps this is just the result of crossover between CG and ML/Statistics here). Not a good sell, but perhaps someone with more experience can chime in.
jfarmer 13y ago
Much of computer graphics operates in projective space (http://en.wikipedia.org/wiki/Projective_space http://en.wikipedia.org/wiki/Projective_space), so it's a little bit more than cookie-cutter linear algebra. This is done so that translations in 3D space — which aren't linear transformations — can be represented as 4D linear transformations in projective space via homogeneous coordinates (http://en.wikipedia.org/wiki/Homogeneous_coordinates http://en.wikipedia.org/wiki/Homogeneous_coordinates). Still, many folks use the APIs without really grokking that, so in practice it can be a bit cookie-cutter. I think of it similarly to how people can use crypto APIs without, say, really understanding what's going on under the hood. BTW, projective space is also intimately related to elliptic curves (as you may or may not know — not implying anything!). So that darn linear algebra is lurking all over the place. Likewise, any time you're talking about fields (even finite fields), vector spaces and linear algebra are right around the corner.
- tptacek 13y ago
  I'm familiar with projective coordinates for elliptic curves, but the funny thing about curves is that, for high-speed software, the math is tricky enough that you don't "need" to grok it: there's an "explicit formulas database" that you can just copy from: http://www.hyperelliptic.org/EFD/g1p/index.html http://www.hyperelliptic.org/EFD/g1p/index.html Curves are what made algebra 'click' for me, getting me from my high school understanding of "algebra is math about unknown variables" to "algebra is about sets of related objects with operators that have identities and inverses".