# Einstein-Notation: rot(rot(A))

## Homework Statement

Write $$\nabla \times (\nabla \times \vec A)$$ in Einstein-Notation, whereas $$\vec A$$ is the vector potential of the magnetic field.

## Homework Equations

$$(\vec a \times \vec b)=\varepsilon_{ijk} a_j b_k$$

## The Attempt at a Solution

$$\nabla \times (\nabla \times \vec A)=\varepsilon_{ijk} \partial_j(\varepsilon_{lmn}\partial_m A_n)_k$$

What to do with $$(\varepsilon_{lmn}\partial_m A_n)_k$$ though?

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## Homework Equations

$$(\vec a \times \vec b)=\varepsilon_{ijk} a_j b_k$$
On the right hand side, there is summation over j and k, but i is a free index which only occurs once. What you really meant to write, then, is

$$(\vec a \times \vec b)_i=\varepsilon_{ijk} a_j b_k$$