Before revision:  4 quaternion-based matrix, thus specifying the quaternion eigenvector corresponding to the optimal 3D rotation. Here we generalize this basic problem , sometimes referred to as the " Procrustes Problem, " and present algebraic solutions that exhibit properties that are inaccessible to traditional numerical methods.
After revision:  4 quaternion-based matrix, thus specifying the quaternion eigenvector corresponding to the optimal 3D point data, this " Procrustes Problem, " and present algebraic solutions that exhibit properties that are inaccessible to traditional numerical methods.