Rotations in 4-dimensional Euclidean space

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In mathematics, the group of rotations about a fixed point in four-dimensional Euclidean space is denoted SO(4). The name comes from the fact that it is the special orthogonal group of 4 by 4 real matrices. In this article rotation means rotational displacement. For the sake of uniqueness, rotation angles are assumed to be in the segment [0, π] except where mentioned or clearly implied by the context otherwise. A "fixed plane" is a plane for which every vector in the plane is unchanged after the rotation. An "invariant plane" is a plane for which every vector in the plane, although it may be affected by the rotation, remains in the plane after the rotation.

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