# Epsilon delta rule states

1. May 4, 2009

### revolution200

The epsilon delta rule states

[TEX]\epsilon_{ijk}\epsilon_{pqk}=\delta_{ip}\delta_{jq}-\delta_{iq}\delta_{jp}[/TEX]

I am constantly using this but get stuck when it is applied.

For example

[TEX]\epsilon_{ijk}\epsilon_{pqk}A_{j}B_{l}C_{m}=(\delta_{ip}\delta_{jq}-\delta_{iq}\delta_{jp})A_{j}B_{l}C_{m}[/TEX]

This then becomes

[TEX]A_{j}B_{i}C_{j}-A_{j}B_{j}C_{i}[/TEX]

Can anybody please explain this result????

Is it true that

[TEX]\delta_{ij}a_{i}=a_{j}[/TEX]

If so does this not apply to the above

Last edited: May 4, 2009
2. May 4, 2009

### DrGreg

Re: Epsilon-delta?

Just replace the word MATH by TEX. You can go back and edit your previous post within 24 hours (I think) of posting it.