Jun 26, 2025 · Quaternions. For me, the quaternions are a 4D algebra $\Bbb H=\Bbb R\oplus\Bbb R^3$ and every quaternion is uniquely expressible as a sum of a scalar and a 3D vector.

May 27, 2020 · How many questions about understanding quaternions have you read on the site? This is something that people are constantly asking about, so there is plenty of material. If …

Unit quaternions can be identified with rotations of three-dimensional space, which is often the best way to think about them. Specifically, take a point in the three-dimensional sphere. If it's …

How does one find the angle difference between two quaternions. There was an answer to this post which says the angle difference between $x$ and $y$ is $z=x\ast \mathrm {conj} (y)$.

Oct 25, 2016 · The first thing that you need to realize is that the concept of an average does not directly apply here. This is for two reasons (1) rotations are not vectors and therefore they do …

Yes ,the question is the basic of the real-number matrix form of quaternions which is I really want to know next step.

There are quaternions and octonions and even sextonions but what about trinonions, quinonions and septonions. Are there 3, 5, and 7 dimensional algebras which could be called trinonions, …

linear-algebra matrices ordinary-differential-equations matrix-equations quaternions Share Cite edited Sep 7, 2014 at 17:11

I'm trying to rotate a 4 dimensional point (w,x,y,z). So far I've been rotating around planes (wx,xy,yz,zw,wy, and xy), but the order in which I do these rotations changes the results and …

Quaternions are a way of specifying a rotation through a axis and the cosine of half the angle. They main advantage is I can pick any two quaternions and smoothly interpolate between …