gives the Hodge dual of the tensor
dualizes tensor in the slots with dimension dim
dualizes tensor in the given slots.
- HodgeDual[tensor] requires all slots of tensor to have the same dimension dim, which will be taken as the implied second argument. The result will have rank dim-r, where r is the rank of tensor.
- HodgeDual[tensor,dim] dualizes tensor in all slots with the given dimension, leaving the rest as the last slots of the result.
- HodgeDual[tensor,dim,slots] requires the given slots of tensor to have dimension dim.
- HodgeDual effectively antisymmetrizes in advance the slots to be dualized.
Examplesopen allclose all
Basic Examples (2)
HodgeDual of a symbolic array:
Properties & Relations (6)
Hodge duality can also be computed by contraction with the LeviCivitaTensor:
Cross of vectors in dimension is ( times the Hodge dual of their tensor product:
Similarly, the Cross of vectors in dimension is simply the Hodge dual of their wedge product:
Wolfram Research (2012), HodgeDual, Wolfram Language function, https://reference.wolfram.com/language/ref/HodgeDual.html.
Wolfram Language. 2012. "HodgeDual." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/HodgeDual.html.
Wolfram Language. (2012). HodgeDual. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/HodgeDual.html