Tensor product of arrays:

Tensor product of symbolic expressions:

Expand linearly:

Compute properties of tensorial expressions:

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:

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: