orthogonal 3x3 matrix may be written as , in which is proper orthogonal. That is, any improper orthogonal 3x3 matrix may be decomposed as a proper rotation (from which an axis of rotation can be found as described above) followed by an inversion (multiplication by -1). It follows that the rotation axis of is also the eigenvector of corresponding to an eigenvalue of -1.

Rotation plane

As much as every tridimensional rotation has a rotation axis, also every tridimensional rotation has a plane, which is perpendicular to the

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