Mathematics-Online lexicon: Epsilon Tensor

	[home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff]
	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.

see also:

Keyword: Vector operation: cross product
Keyword: Epsilon tensor

[Examples]

automatically generated 3/28/2008