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In this paper we provide an alternative characterization of entanglers, whichare unitary matries that transform local qubit gates into special orthogonalmatrices via the adjoint action. Our alternative characterization invovles aproperty which we refer to as the "reverse dot product identity," which we showhas various applications. In particular, we use the reverse dot productidentity to prove that the change of basis matrix from the computational basisto the Bell gems (a proposed generaliztion of the Bell basis), are entanglers,and we also reveal a close connection between the reverse dot product identityto the $n$-tangle and use this to provide sufficient conditions for when amixed state is spin-invariant.

Alternative Characterization of Entanglers and Some Applications