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Levi-Civita symbol as a tensor

Ciro Santilli (@cirosantilli, 37) ... Mathematics Area of mathematics Algebra Linear algebra Index picking function Levi-Civita symbol
Updated 2025-07-16  0 By others on same topic  0 Discussions Create my own version
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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 (ei​,ej​,ek​) and a function that return the volume of a parallelepiped given by three vectors V(v1​,v2​,v3​), εikj​=V(ei​,ej​,ek​).

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