On Sun, Nov 1, 2020 at 7:35 PM Dan Asimov <dasimov@earthlink.net> wrote:
Henry Baker wrote
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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.
What is meant by rotation on a 2-dimensional plane? Do you mean that there's a codimension-2 subspace that is fixed, and rotation in the other two coordinates, so that the matrix (in a suitable basis) looks like a 2x2 rotation matrix, and then 1's on the rest of the diagonal, and zeroes everywhere else? 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
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