HodgeDual

HodgeDual[tensor]

gives the Hodge dual of the tensor

HodgeDual[tensor,dim]

dualizes tensor in the slots with dimension dim

HodgeDual[tensor,dim,slots]

dualizes tensor in the given slots.

Details

  • 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.

Examples

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Basic Examples  (2)

Hodge dual of a three-dimensional vector:

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Hodge dual of a scalar in dimension three:

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Scope  (5)

Properties & Relations  (6)

See Also

TensorWedge  LeviCivitaTensor  SymmetrizedArray  Symmetrize  Cross  Antisymmetric

Tutorials

Introduced in 2012
(9.0)