# Tagged Questions

For questions about the quaternions: a noncommutative four dimensional division algebra over the real numbers.

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### 4-D lattices and quaternions

It is easy to prove that there are only 2 extensions $\mathbb{Q}(a)$, with $|a|=1$, of $\mathbb{Q}$ where $\mathbb{Z}[a]$ becomes a lattice(discrete free abelian subgroup of rank 2) in the complex ...
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### Angle between Quaternions

I am busy with a project where I have to calculate the angle between 2 quaternions. The inner workings of the project are: There is a reference quaternion and every other quaternion I encounter will ...
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### can somone exaplin how the equations for quanterion roation actually work, or at least show me some?

I don't know enough about qunaterion rotation to as the question easily. Sufficient to say I have a system were three rectangles on a 2 axis plan (I think those words are right.....) that are ...
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### How can I visualize Quaternion Linear Interpolation?

It’s hard enough to visualize a quaternion, geometrically speaking. A complex number is simple: it’s a point in a plane. Suppose we had a number like this: a + bi + cj I supose you can visualize ...
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### Multiplying quaternions vs multiplying rotation matrices

It's a trivial question, but one I'm not 100% clear about. Given two matrices $$P_{\{1,2\}} = \left[ \begin{array}{cc}R & t \\ \textbf{0} & 1 \end{array}\right]$$ where $R$ is a 3x3 ...
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### Possibilities for $\deg f$ if $\text{Gal}(f/\mathbb{Q})=Q_8, D_8$

Let $f$ be irreducible over $\mathbb{Q}$ with splitting field $F$. Suppose $\text{Gal}(F/\mathbb{Q})$ is either $D_8$ or $Q_8$. What are the possibilities for $\deg f$? I'm using Dummit & Foote,...
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### Estimate angular velocity and acceleration from a sequence of rotations

I have a set of rotations: $R(t) \in R^{3x3}, t = 1, 2, ... T$. I can extract the orientation of a body $\theta (t)$ from the rotation matrix $R(t)$. I am interested to estimate the angular ...
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### Unit quaternion multiplied by -1

If all components of a unit quaternion (also known as versor) are multiplied by -1, so it still remains a versor, does the resulting versor is considered equivalent to the original versor?
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### Quaternion Rings

Let $R$ be a commutative ring. Define the Hamilton quaternions $H(R)$ over $R$ to be the free $R$-module with basis $\{1, i, j, k\}$, that is, $$H(R)=\{a_0+a_1i+a_2j+a_3k\;\;:\;\;a_l\in R\}.$$ and ...
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### Why are There No “Triernions”? [duplicate]

Since there are complex numbers (2 dimensions) and quaternions (4 dimensions), it follows intuitively that there ought to be something in between for 3 dimensions ("triernions"). Yet no one uses ...
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### Rotation about z axis using quaternions

I am working with quaternions and rotation, but I am missing something about how a rotation expressed as a quaternion works. I also discovered that there are different convention for quaternions (JPL, ...
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### Can you extract the horizontal component of the change of two quaternions?

I receive orientation data as quaternions, and I'm interested in finding the ground-planed component of the change in angle. I know that the arccosine of the dot product of two quaternions gives me ...
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### Difference between quaternions depends on initial rotation

The difference $\Delta q$ between two quaternions $q1$ and $q2$ can be calculated as $\Delta q = q1\cdot q2^{-1}$, where $^{-1}$ is the quaternion conjugate. When numerically evaluating the ...