
Ask HN: What should I know about linear Algebra, and where will I use it? - ColinWright
People say that Linear Algebra is used all over machine learning, and other hot topics, but I rarely see actual case studies, or explanations of actual examples.<p>I'm pretty sure Linear Algebra isn't used in most web or CRUD applications, so where have <i>you</i> seen it in action?<p>What should I know about Linear Algebra?
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thejteam
Google pagerank:

<http://www.ams.org/samplings/feature-column/fcarc-pagerank>

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27182818284
One of the best answers to "when while I ever use this stuff?" a teacher could
provide, even when in high school.

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6thSigma
Graphics. You'll see it especially in game development.

If you can comprehend thinking in multi dimensions you should be fine.
Obviously you'll need to learn matrix arithmetic.

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ColinWright
How does Linear Algebra feature in game development? Can you provide a
reference? My Google-fu must be lacking today ...

Thanks.

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sopooneo
Say you know the coordinates of all the corners of a cube in three dimensions.
If you wanted to move that cube to the side and turn it, you could first add
some fixed number to all the x coordinates of every point, then do some trig
to find the coordinates again after a rotation. Turns out you can produce the
same output with fewer steps using matrix math. That is, you can produce a
single matrix which is representative of the transform "move right m units and
turn d degrees". And you can apply that transform matrix to any set of points
you want.

At least, this is what I've gleaned so far as someone that doesn't really
understand. I welcome corrections.

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ColinWright
That's the best answer I've had so far, but it seems like it's just talking
about matrix operations. There doesn't really seem to be any "proper" Linear
Algebra in here. Nothing about bases, change of bases, null spaces, proofs
that all bases have the same size, eigen-values and eigen-vectors, none of the
juicy stuff. Just matrix multiplication.

So I was wondering if the more advanced stuff is used, or if it really is just
the dabbling in the shallows.

Thanks.

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mjn
I wrote a short introduction to some of the projection math used in 3d
graphics, which gets _slightly_ into it, though not into greatly juicy stuff:
<http://www.kmjn.org/notes/3d_rendering_intro.html>

Beyond just matrix arithmetic, a change of basis is usually used in viewing,
to change an x-y-z "world" coordinate space into a u-v-w camera-relative
coordinate space (discussed in the "View space" section).

The homogeneous coordinates used to encode affine transforms into matrix
multiplications also have a rigorous linear-algebra background, but admittedly
they can be treated as just a strange hack (use a "dummy" 4th dimension for 3d
coordinates) without really needing the theory.

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dgunn
I'm using linear algebra in a CRUD app. In short, the app generates a lot of
math problems. I use some of the more basic aspects of linear algebra to do
this. Matrix equations, etc.. Linear algebra is used extensively in certain
types of software like etap, pspice, etc.. Anything where systems can be
represented by systems of equations will usually benefit from employing matrix
operations.

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27182818284
<http://en.wikipedia.org/wiki/Eigenface> comes to mind

also <http://en.wikipedia.org/wiki/Singular_value_decomposition> seems to pop
up every couple of months or so in a "Oh they do that with SVD?" way

