# Tagged Questions

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### Show exponential function maps any line through the origin onto a circle of radius 1 in $\mathbb{S}^3$.

Show that the exponential function maps any line through the origin in $\mathbb{R}$i +$\mathbb{R}$j + $\mathbb{R}$k onto a circle of radius 1 in $\mathbb{S}^3$. I know that for any element v $\in$ ...
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### How to Perform Quaternion Multiplication

Everywhere that I've looked, it seems to be assumed that $i^{2} = j^{2} = k^{2} = - 1$, along with the other rules of quaternion multiplication. However - for my homework - I'm being asked to show ...
Hurwitz quaternions are defined as: $$H_u = \left\{a+bi+cj+dk\mid (a,b,c,d) \in\mathbb{Z}\mbox{ or }(a,b,c,d) \in\mathbb{Z}+\frac{1}{2}\right\}$$ (that is, all integer or half integer quaternions). ...
### what is the tensor product $\mathbb{H\otimes_{R}H}$
I'm looking for a simpler way of thinking about the tensor product: $\mathbb{H\otimes_{R}H}$, i.e a more known algbera which is isomorphic to it. I have built the algebra and played with it for a ...