The dual tensor 
of an antisymmetric tensor 
of tensor rank 2 in three
dimensions is a pseudovector defined by
 |
(1)
|
where 
is the permutation
symbol and
 |  | ![[C_(23); C_(31); C_(12)]](/images/equations/DualTensor/Inline6.svg) |
(2)
|
 |  | ![[0 C_3 -C_2; -C_3 0 C_1; C_2 -C_1 0].](/images/equations/DualTensor/Inline9.svg) |
(3)
|
Dual Tensor
See also
Dual ScalarExplore with Wolfram|Alpha
References
Arfken, G. "Pseudotensors, Dual Tensors." §3.4 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 128-137, 1985.Referenced on Wolfram|Alpha
Dual TensorCite this as:
Weisstein, Eric W. "Dual Tensor." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DualTensor.html