Dual Scalar

Given a third Rank Tensor,

$$V_{ijk} \equiv \mathop{\rm det}\left[{\matrix{{\bf A} & {\bf B} & {\bf C}\cr}}\right],$$

where det is the Determinant, the dual scalar is defined as

$$V \equiv {1\over 3!} \epsilon_{ijk}V_{ijk},$$

where $\epsilon_{ijk}$ is the Levi-Civita Tensor.

See also Dual Tensor, Levi-Civita Tensor