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it is a clear fact that rotations in 3D keep the vectors on the rotation axis unchanged.

In 2D only the zero vector is unchanged.

How can one generalize the concept of rotation axis in N-dimensions?

I've read that for example in 4D one can only rotate around planes.

So are the rotation "hyper-axes" always subspaces of dimensionalityn-2?

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# N-dimensions rotation axes

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