Tensor Product
Let X and Y be two K-vector spaces. The tensor product X ⊗ Y from X and Y is a K-vector space Z with a bilinear function T: X × Y → Z which has the following universal property: If T′: X × Y → Z′ is any bilinear function into a K-vector space Z′, then only one linear function f: Z → Z′ with exists.
There are various norms that can be placed on the tensor product of the underlying vector spaces, amongst others the projective cross norm and injective cross norm. In general, the tensor product of complete spaces is not complete again.
Read more about this topic: Banach Space
Famous quotes containing the word product:
“The UN is not just a product of do-gooders. It is harshly real. The day will come when men will see the UN and what it means clearly. Everything will be all right—you know when? When people, just people, stop thinking of the United Nations as a weird Picasso abstraction, and see it as a drawing they made themselves.”
—Dag Hammarskjöld (1905–1961)