Can anyone explain quaternions?

Can anyone explain quaternions?

Other urls found in this thread:

en.wikipedia.org/wiki/Quaternion#Scalar_and_vector_parts
twitter.com/AnonBabble

i^2=j^2=k^2=ijk=-1, and they're noncommunative.

What more do you need to know?

What does that mean?

Take all three [math]\frac\pi2[/math] rotation matrices in a 3D space and call them [math]\mathrm i[/math], [math]\mathrm j[/math] and [math]\mathrm k[/math]. Then identify the identity matrix with 1. Done.

Noncommunative means (a*b) does not necessarily equal (b*a)

What does * mean?

Multiplication

quarternion: 3dim vector + 1dim strength

the good stuff is that adding rotation just means adding them together and normalizing

Yes, YouTube can.
Sure, everyone here will call it pop-sci, whatever. There are actually a couple of videos that will give you a little intuition about quaternions. Truth is, though, they're just not very intuitive things. But they're useful.

I think you mean non-commutative.

True haha, fucking letters, how do they work

it's pretty easy really

Those are vectors

Yes they are.
en.wikipedia.org/wiki/Quaternion#Scalar_and_vector_parts

I read somewhere that Hamilton's idea was to get a 3D version of the complex plane by having two independent imaginary units satisfying [math]i^2 = -1 = j^2[/math], but what would [math]ij[/math] be then? If [math]ij= \pm 1[/math], then [math]i = \pm j[/math], contradicting the independence assumption, and if [math]ij= \pm i[/math] or [math]ij = \pm j[/math], then [math]j = \pm 1[/math] or [math]i = \pm 1[/math], respectively, but these contradict the assumption that we have imaginary units. Therefore, he got an idea: he would add a third unit there to satisfy the equation [math]ij=k[/math].

Using these three units, one can see the following equations [math]ij = k \Leftrightarrow i = k(-j)=-kj[/math] and [math]j = -ik[/math], which lead to [math]k^2 = ijij=i(-k)j=-ikj=j^2 =-1[/math] and so [math]ijk = -1[/math]. It follows that Hamilton's idea works with three imaginary units connected via the relation [math]i^2 = j^2 = k^2 = ijk = -1[/math].

So the Veeky Forums verdict on quaternions is:

>quarternion: 3dim vector + 1dim strength
>i^2=j^2=k^2=ijk=-1, and they're noncommunative.

Great stuff

that's not Veeky Forums verdict as much as just their literal defining quality.

>Therefore, he got an idea: he would add a third unit there to satisfy the equation ij=kij=kij=k.
this is natural, so why did he take so long to get them?

Something tells me this is the only place you'll read that quarternions are non communative though

...

Most useful explanation for laymen is you're flying a jet in 3d space, so your forward motion is a 3 number vector. Now you need to do a barrel roll or a hard bank. So to track your rotation too we need a 4 number vector and that's the quaternion. It's a pretty awesome name for an otherwise simple concept.

>Being this dyslexic

Do you really think nobody else makes spelling mistakes in mathematics?

Fuuuckkkk, again. Fucking letters, how do they work