Which rotations Cannot commute?
Which rotations Cannot commute? Two rotations sometimes commute. In 2D rotations do commute, while in 3d most pairs of rotations do not commute. Why are 3D rotations not commutative? Rotations in three dimensions are generally not commutative, so the order in which rotations are applied is important even about the same point. Rotations about the origin have three degrees of freedom (see rotation formalisms in three dimensions for details), the same as the number of dimensions. What is finite rotation? SO(n) is a subgroup of O(n), the group of distance-preserving linear transformations of a Euclidean space including rotations and reflections,...