represents the tensor product of the tensori.
- TensorProduct[a,b] can be input as ab. The character is entered as t* or \[TensorProduct].
- The tensor product a1…an of rectangular arrays ai is equivalent to Outer[Times, a1,…,an].
- The tensor product t1…tn of arrays and/or symbolic tensors is interpreted as another tensor of rank TensorRank[t1]+…+TensorRank[tn].
- TensorProduct returns 1. TensorProduct[x] returns x.
- TensorProduct is an associative, non-commutative product of tensors.
Examplesopen allclose all
Basic Examples (2)
Tensor product of arrays of any depth and dimensions:
Product of symmetrized arrays, with the result also in symmetrized form:
The fact that both arrays are the same adds more symmetry:
There are only six nonzero independent components:
Tensor product of symbolic expressions:
Tensor product of objects of different types. Contiguous arrays are multiplied:
Properties & Relations (11)
The tensor product is not commutative:
The difference is always some transposition:
The tensor product of arrays is equivalent to the use of Outer:
The KroneckerProduct of vectors is equivalent to their TensorProduct:
The KroneckerProduct of matrices is equivalent to the flattening of their TensorProduct to another matrix:
The KroneckerProduct of any two arrays is also equivalent to a flattening of their TensorProduct:
The rank of a tensor product is the sum of ranks of the factors:
The tensor product of a tensor with itself gives a result with added symmetry:
TensorProduct[x] returns x irrespectively of what x is:
TensorProduct is 1:
Obvious scalars are extracted from a tensor product:
Symbolic scalars need to be specified with assumptions:
TensorProduct has Flat attribute:
TensorProduct, in combination with TensorContract, can be used to implement Dot:
Antisymmetrization of TensorProduct is proportional to TensorWedge:
Wolfram Research (2012), TensorProduct, Wolfram Language function, https://reference.wolfram.com/language/ref/TensorProduct.html.
Wolfram Language. 2012. "TensorProduct." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/TensorProduct.html.
Wolfram Language. (2012). TensorProduct. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TensorProduct.html