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
R3, 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
ijkb
jc
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
ijkA
1iA
2jA
3k