Euler's Rotation Theorem

Euler's rotation theorem is a result in geometry stating that any displacement of a rigid body in three dimensional space that leaves one point fixed is equivalent to a single rotation about some axis running through that fixed point. Leonhard Euler proved the result in 1775 using spherical geometry. Composing two such rotations yields another rotation, giving the set of rotations a group structure known as the rotation group, and in linear algebra terms a non identity rotation matrix has one eigenvalue equal to one, whose eigenvector marks the axis of rotation, with the other two eigenvalues either complex conjugates or both equal to minus one. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/