Mathematics-Online lexicon: Epsilon Tensor

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	Mathematics-Online lexicon:
	Epsilon Tensor

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overview

The tensor

$\displaystyle \varepsilon_{i,j,k}\in\{-1,0,1\},\quad i,j,k\in\{1,2,3\}\, ,$

equals zero if two indices are the same. Otherwise, it has the following values:

$\begin{displaymath} \begin{array}{cc cc cc c} \varepsilon_{1,2,3} &=& \vareps... ...ilon_{2,1,3} &=& \varepsilon_{3,2,1} &=& -1\,. \end{array} \end{displaymath}$

Thus it is invariant with respect to cyclic permutation of indices and changes its sign if indices are interchanged.

Example:

Example: Vector Product by Means of the Epsilon Tensor

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automatically generated 3/28/2008