The title of the node is mean to read ε

_{ijk}, but node titles cannot contain subscripts.

Anyway, ε

_{ijk} is a third rank

tensor on

**R**^{3}, which takes the value 1 when (ijk) is an even

permutation of (123) (ie. (123),(231),(312)), the value -1 if (ijk) is an odd permutation of (123) (ie. (321),(213),(321)), and is zero if otherwise.

It is used for expression vector products in

abstract index notation, eg

**a**=

**b**×

**c** becomes a

_{i}=ε

_{ijk}b

_{j}c

_{k}, similarly for

curl **b** if you replace

**a** by

nabla and a

_{j} by partial-d-by-dx

_{j}.

You can also write the

determinant of a 3×3

matrix **A** as ε

_{ijk}A

_{1i}A

_{2j}A

_{3k}