# Questions tagged [quaternions]

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

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### Geodesic of quaternion swings vs vector angle

Context I work on calculating distance between quaternions, the idea at the end is to train a machine learning algorithm to estimate a rotation in quaternion. I have two quaternions $Q_1$ and $Q_2$ ...
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### Numeric system where iterated square roots of 1 have integer parts

Let us define $s(n)$ as any solution to the equation $x^2 = n$, such that $x \neq n$. I am looking for a numeric system such that $s(s(s\cdots s(1)))$ is always an integer or is composed of integer ...
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### Unitary groups and special unitary groups

I'm trying to learn about group theory (I'm neofite in this field) for physics reading a book, "Physics from symmetry" by Schwichtenberg. In section 3.2 the author introduces rotations in ...
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### Basis of the matrix representation of a quaternion

I'm trying to learn some group theory for physics as a self-learner. I'm reading about rotation in 2D and 3D space. The book I'm following, Physics from symmetry by Schwichtenberg, firstly proves that ...
• 63
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### Commutate a Quaternion multiplication

I have a fixed Quaternion t that is defined as Quaternion([0.5, -0.5, -0.5, 0.5]);. The order here is ...
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### Finding the quaternion which projects one vector onto another

I'm currently working on a program that requires specifying a quaternion rotation to point a cylinder in the direction of its velocity vector, i.e. projecting the $z$-axis onto that velocity vector. ...
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It's known that there are four non-abelian groups with cyclic subgroup of index $2$. Those groups are the dihedral group $D_{2^n}$, generalised quaternion group $Q_{2^n}$, modular-maximal group \$M_{2^...