 The choice of basis vectors is dictated by the symmetry properties of the space and, in general, these basis vectors are not orthogonal (so that the matrix η"ab" is not diagonal).The reciprocal triple of vectors formula_4 is introduced with the help of Kronecker delta
In the three-dimensional case, the relation between the two vector triples can be written explicitly

where the volume "v" is

with e("a") and e("a") regarded as Cartesian vectors with components formula_4 and formula_7, respectively.The determinant of the metric tensor is γ = η"v"2 where η is the determinant of the matrix η"ab".