[ V ^ ^ a , J ^ ^ b ] = ∑ ∑ c i ℏ ℏ ε ε a b c V ^ ^ c where ε ijk is the Levi-Civita symbol, which all vector operators must satisfy, by construction. The above commutator rule can also be used as an alternative definition for vector operators which can be shown by using the Baker Hausdorff lemma. As the symbol ε ijk is a pseudotensor, pseudovector operators are invariant up to a sign: +1 for proper rotations and −1 for improper rotations.