Re: [math-fun] Quaternion eigenvectors, Part Deux

Henry Baker wrote ----- It is also well known that every 4D rotation can be expressed as the *independent* rotations of 2 planes orthogonal to one another, each with their own separate rotation. ----- In fact any rotation of R^n (orientation-preserving isometry taking the origin to itself) is in fact the result of floor(n/2) rotations on mutually orthogonal 2-dimensional planes. If the angles are all distinct and not 0 or π, then this decomposition is unique. Coxeter wrote a great paper on quaternions and rotations and reflections of 4-dimensional space: "Quaternions and Reflections", the Monthly, Vol. 53, No. 3 (Mar., 1946), pp. 136-146. —Dan