# A really easy question on properties of the Levi-Civita tensor and index interchange

1. Feb 28, 2009

### AxiomOfChoice

Does the following identity hold?:

$$\epsilon_{ijk} a_j b_k = -\epsilon_{ijk} a_k b_j$$

2. Feb 28, 2009

### cristo

Staff Emeritus
Re: A really easy question on properties of the Levi-Civita tensor and index intercha

Yes.

3. Feb 28, 2009

### confinement

Re: A really easy question on properties of the Levi-Civita tensor and index intercha

The answer is yes; clearly we have:
$$\epsilon_{ijk} a_j b_k = -\epsilon_{ikj} a_j b_k$$

from which we can obtain your identity by relabeling the dummy indices j and k.