TensorWedge

TensorWedge[tensor1,tensor2,]

represents the antisymmetrized tensor product of the tensori.

Details

  • TensorWedge[a,b] can be input as ab. The character is entered as t^ or \[TensorWedge].
  • In a tensor wedge product of explicit or symbolic arrays, all slots must have the same dimension , though different arrays may have different ranks. TensorWedge generalizes Cross, which requires vectors of length .
  • The TensorWedge product of several arrays is an antisymmetric array, always given in SymmetrizedArray form.
  • If the tensors tensori are not antisymmetric, then they are effectively antisymmetrized before performing the product. Vectors are considered antisymmetric tensors of rank 1. Scalars are considered antisymmetric tensors of rank 0.
  • The wedge product TensorWedge[t1,,tk] of the antisymmetric tensors ti is equivalent to Multinomial[r1,,rk]*Symmetrize[TensorProduct[t1,,tk],Antisymmetric[All]], where ri is the tensor rank of ti.

Examples

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Basic Examples  (1)

Antisymmetrized tensor product of explicit vectors:

In[1]:=
Click for copyable input
Out[1]=

In normal form:

In[2]:=
Click for copyable input
Out[2]=

Scope  (3)

Properties & Relations  (11)

Possible Issues  (1)

See Also

Cross  TensorProduct  Symmetrize  Det  SymmetrizedArray  HodgeDual

Tutorials

Introduced in 2012
(9.0)