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 , 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.
Introduced in 2012
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