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again to first order. In other words, {{em|the order in which infinitesimal rotations are applied is irrelevant}}.
This useful fact makes, for example, derivation of rigid body rotation relatively simple. But one must always be careful to distinguish (the first-order treatment of) these infinitesimal rotation matrices from both finite rotation matrices and from Lie algebra elements. When contrasting the behavior of finite rotation matrices in the [[Baker–Campbell–Hausdorff formula]] above with that of infinitesimal rotation matrices, where all the commutator terms will be second-order infinitesimals, one finds a bona fide vector space. Technically, this dismissal of any second-order terms amounts to [[Group contraction]].
== Generators of rotations ==
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