What is a tensor product?

Thus, all tensor products can be expressed as an application of the monoidal category to some particular setting, acting on some particular objects.

What is monoidal tensor product?

It captures the algebraic essence of tensoring, without making any specific reference to what is being tensored. Thus, all tensor products can be expressed as an application of the monoidal category to some particular setting, acting on some particular objects.

What are the tensor products of operators ai and AII?

Tensor products of operators If we assume operators AI and AII acting on the Hilbert spaces HI and HII we can derive an operator acting on H = HI ⊗ HII. This operator A is defined by the tensor product A = AI ⊗ AII and acts on the elements of H as following:

Can a tensor product be over a sheaf of differential operators?

One important case when one forms a tensor product over a sheaf of non-commutative rings appears in theory of D -modules; that is, tensor products over the sheaf of differential operators . . Since the image of f is IM, we get the first part of 1.

How do you express the tensor product in APL?

For example, in APL the tensor product is expressed as ○.× (for example A ○.× B or A ○.× B ○.× C ). In J the tensor product is the dyadic form of */ (for example a */ b or a */ b */ c ).

How do you find the tensor product of fields?

The tensor product of fields is closely related to Galois theory: if, say, A = R[x] / f(x), where f is some irreducible polynomial with coefficients in R, the tensor product can be calculated as where now f is interpreted as the same polynomial, but with its coefficients regarded as elements of B.

Is the tensor product of a and B an abelian group?

Then the tensor product of A and B is an abelian group defined by The universal property can be stated as follows. Let G be an abelian group with a map s ( a ⊗ b ) := ( s a ) ⊗ b . {\\displaystyle s (a\\otimes b):= (sa)\\otimes b.}