Can anyone explain quaternions?

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

What more do you need to know?

>>9166082
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.

>>9166237
Noncommunative means (a*b) does not necessarily equal (b*a)

>>9166318
What does * mean?

>>9166328
Multiplication

quarternion: 3dim vector + 1dim strength

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

>>9165968
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.

>>9166082
>>9166318
I think you mean non-commutative.

>>9166432
True haha, fucking letters, how do they work

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it's pretty easy really

>>9166670
Those are vectors

>>9166693
Yes they are.
https://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 /sci/ verdict on quaternions is:

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

Great stuff

>>9168018
that's not /sci/ verdict as much as just their literal defining quality.

>>9166718
>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?

>>9168027
Something tells me this is the only place you'll read that quarternions are non communative though

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>>9168090

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.

>>9168247
>Being this dyslexic

>>9168090
Do you really think nobody else makes spelling mistakes in mathematics?

>>9168018
>>9168090
>>9169432
Fuuuckkkk, again. Fucking letters, how do they work