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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

[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

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