Matrix vector products as linear transformations | Linear Algebra | Khan Academy

Matrix Vector Products as Linear Transformations
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[@hichemhaddouche]

at 3:22 he became a pirate

[@100yearoldpiano3]

or our our or rawr arrg

[@afnanjaved1986]

ahahahaah yeah xD !!

[@ssims619]

thank you so much. I have been trying to figure out linearity all day. I've read the textbook and a bunch of online tutors but now I finally understand!

[@ChunkOfNorris]

I LOVE graphics cards. Great motivation for learning this, besides graduating and getting a job of course.

[@MobiusCoin]

Man, in our 3D Computer Animation class... we were given a set of coordinates and we had to do the linear Transformation so that the 3D "object" projects onto the 2D viewplane by hand... that was a nightmarish exam. It turned out to be a bunny.

[@abdullahyahya2471]

thank you .... you are legends...

[@haterallday]

applying linear algebra to real life application. what a baller

[@s0m0c]

Gracias!

[@MeistroJB]

... I probably don't "run around and shoot at things." I would respectfully recommend that there are better things to do.

[@RNeilen216]

IMO, This is really confusing me. When I am working in 3d space, movement, rotation, and scale, deal with transformation matrices. So how does this video apply to 3d space. For example, what's the new position after an object has been rotated 30 degrees and then translated 5 units further along its forward vector.

[@pavichokche]

you kids and your fancy xboxes and shooting games *shakes cane in diapproval* xD

[@MeistroJB]

can't tell if you're serious.... but respectfully suggest even better things to do, if you can handle it.

[@anguswaterson6741]

@3:21 there is a pirate

[@gbityunan]

When you are talking about matrix being multiplied by a vector and matrix is on the left, shouldn't you be referring to "row vectors" of the matrix instead of "column vectors"? Am I confused?

[@apoorvaverma7705]

The matrix looks like a row vector but the elements in it (v1.........vn) are column vectors themselves which contain m elements.

[@patrickmoloney672]

Is there anything Khan doesn't know? :)

[@mustafasiddiqui8203]

What is life. He don't know

[@davidmurphy563]

Well, scaling is trivial. It's just identity times a scalar. But what about rotation and sheering? Or, more to the point, what about if you wanted to project an R3 vector into an R2 either orthographically or with a perspective component? How do we arrive at useful matrices without it becoming undefined?