BUILT-IN MATHEMATICA SYMBOL

# TensorWedge 

TensorWedge[tensor1, tensor2, ...]
represents the antisymmetrized tensor product of the .

## DetailsDetails

• TensorWedge[a, b] can be input as . The character is entered as Esct^Esc 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 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 is equivalent to Multinomial[r1, ..., rk]*Symmetrize[TensorProduct[t1, ..., tk], Antisymmetric[All]], where is the tensor rank of .

## ExamplesExamplesopen allclose all

### Basic Examples (1)Basic Examples (1)

Antisymmetrized tensor product of explicit vectors:

 Out[1]=

In normal form:

 Out[2]=