WOLFRAM|DEMONSTRATIONS PROJECT

Product of Two Levi-Civita Tensors with Contractions

​
rank of the Levi-Civita permutation tensor
2
3
4
5
number of contracted indices
0
1
2
3
allow dynamic resizing
ε
abc
ε
ijk
= -
δ
a,k
δ
b,j
δ
c,i
+
δ
a,j
δ
b,k
δ
c,i
+
δ
a,k
δ
b,i
δ
c,j
-
δ
a,i
δ
b,k
δ
c,j
-
δ
a,j
δ
b,i
δ
c,k
+
δ
a,i
δ
b,j
δ
c,k
The product of two Levi-Civita tensors is a sum of products of Kronecker deltas.