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which would make the 4-D component 0.

To be honest I'm not really sure how 4-D rotations work. I know about the simple rotations but not the mechanism in how it rotates, and I'm not sure whether to use a simple or a double rotation in this case. Other than that I can do rotations in less than 4 dimensions.

If someone is aware of an additional piece of information, that would help solve my whole problem, would be the the transformation of a unit vector along one of the axes into the long diagonal of a unit hypercube. The scaling is easy (multiply by $\sqrt{d}$) for any dimension $d$ but I can't get the rotation down.

Thanks in advance.

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  • $\begingroup$ I'm sorry, but what exactly is your question? $\endgroup$
    – HSN
    Apr 15, 2015 at 22:27
  • $\begingroup$ sorry, edited the post $\endgroup$
    – Chris Wang
    Apr 15, 2015 at 23:18
  • $\begingroup$ 4D as in Minkowski space, or 4D as in homogeneous coordinates? $\endgroup$ Mar 8, 2017 at 14:40

1 Answer 1

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If I understand your question, you want to find a 4-D rotation matrix $R$ such that $$R\begin{bmatrix}0\\ 0\\ 0\\ 1\end{bmatrix} = \frac 12\begin{bmatrix}1\\ 1\\ 1\\ 1\end{bmatrix}.$$ To calculate $R$, see here and here.

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