Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag

Mathematics-Online lexicon:

Epsilon Tensor


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 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.
[Examples] [Links]

  automatically generated 3/28/2008