- #1

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[itex]\sum[/itex]

_{j}[itex]\sum[/itex]

_{k}ε

_{i,j,k}∂

_{j,k}

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- Thread starter tolove
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- #1

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[itex]\sum[/itex]

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- #3

Mark44

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Minor pedantic point: The word is "typo", which is short for typographical error.

- #4

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^{th}component of a vector. However, since δ_{jk}is zero if j≠k and ε_{ijk}is zero if j=k, this is a complicated way of writing the zero vector.

Thank you very much! The i isn't being defined because it doesn't matter what i is in this situation.

And to mark... I didn't know that, thanks

- #5

Ray Vickson

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[itex]\sum[/itex]_{j}[itex]\sum[/itex]_{k}ε_{i,j,k}∂_{j,k}

No typo: the standard ε-symbol, used, eg., in writing vector cross-products in 3 dimensions, is:

[tex] \epsilon_{i j k} = \left\{ \begin{array}{rccl}

1 &\text{ if }& ijk &\text{ is an even permutation of 123}\\

-1&\text{ if }&ijk & \text{ is an odd permutation of 123}\\

0 &&&\text{ otherwise }

\end{array} \right. [/tex]

So, for example, the ith component of ##\vec{C} = \vec{A} \times \vec{B}## is ##C_i = \sum_{j,k} \epsilon_{ijk} A_j B_k##.

BTW: 'type-o' is a category of blood (for blood donations); what you probably mean is 'typo'.

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