Question

What is th difference between direct sum and tensor product?

Answer 1

In mathematics, the tensor product V ⊗ W of two vector spaces V and W (over the ... In particular, this distinguishes the tensor product from the direct sum vector space.

Answer 2

Both direct sum and tensor product are standard ways of putting together little Hilbert spaces to form big ones. They are used for different purposes. Suppose we have two physical systems A and A', with Hilbert spaces H and H'.