Kronecker Delta/Alternating Tensor Question

**craig** · March 8th 2011, 01:58 AM

Hi, just a quick question on an identity involving the Kronecker Delta and the Alternating Tensor.

Just checking that I've got this right.

Simplify $\epsilon_{ijk} \epsilon_{pjk}$

I get:

$\epsilon_{ijk} \epsilon_{pjk} = \delta_{ip} \delta_{jj} - \delta_{ij} \delta_{jp}$

$= 3 \delta_{ip} - \delta_{ij} \delta_{jp}$

$= 3 \delta_{ip} - \delta_{ip}$

$= 2 \delta_{ip}$

Is this the answer in it's simplest form?

Thanks in advance

**Ackbeet** · March 8th 2011, 04:46 AM

Looks good to me!

**craig** · March 8th 2011, 08:39 AM

Thankyou

**Ackbeet** · March 8th 2011, 08:43 AM

You're welcome!

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