Ciro Santilli @cirosantilli 34

An Introduction to Tensors and Group Theory for Physicists by Nadir Jeevanjee (2011) shows that this is a tensor that represents the volume of a parallelepiped.

It takes as input three vectors, and outputs one real number, the volume. And it is linear on each vector. This perfectly satisfied the definition of a tensor of order (3,0).

Given a basis $(e_i,e_j,e_k)$ and a function that return the volume of a parallelepiped given by three vectors $V(v_1,v_2,v_3)$, ${\epsilon }_{ikj}=V(e_i,e_j,e_k)$.