represents the antisymmetrized tensor product of the tensori.
- 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.
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Properties & Relations (11)
The proportionality factor is the Multinomial of the ranks:
For vectors of length , the only independent component of their TensorWedge equals the determinant of the list of those vectors: