Solving Confusion with Summation Convention - Ian

[iansullivan88]

Hello, I think I am fundamentally confused with summation convention. For example, if I have

$\epsilon_{ijk}x_j\delta_{jk}$

Can I sift the levi civita and get

$\epsilon_{ijj}x_j=0$

or sift x and get

$\epsilon_{ijk}x_k\not=0$

Each gives a different answer. What mistake am I making here?
Thank you,

Ian

 

[cristo]

The fundamental confusion is that you've got an index repeated three times. This is incorrect: an index can only appear once or twice, the latter meaning it is summed over.

 

[iansullivan88]

Ah I see - thanks very much

Ian