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Epsilon Tensor

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The tensor

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

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

\begin{array}{cc cc cc c}
\varepsilon_{1,2,3} &=&
...ilon_{2,1,3} &=&
\varepsilon_{3,2,1} &=&

Thus it is invariant with respect to cyclic permutation of indices and changes its sign if indices are interchanged.
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  automatically generated 3/28/2008