This is a beginner's question on what exactly is a tensor product, in laymen's term, for a beginner who has just learned basic group theory and basic ring theory. I do understand from wikipedia …

The Tensor Product, Demystified is the clearest explanation I've read to-date. And I've read at least a dozen other explanations (including the answers here) and took a class that covered …

Jan 25, 2011 · Can anyone explain me as to why Tensor Products are important, and what makes Mathematician's to define them in such a manner. We already have Direct Product, Semi …

Jun 22, 2015 · From memory, the direct sum and direct product of a finite sequence of linear spaces are exactly the same thing. Maybe they differ, according to some authors, for an …

The first definition comes from the philosophy that students are bad at understanding abstract definitions and would prefer to see the tensor product defined as a space of functions of some …

It can't be true in general, because rank-1 elements of the tensor product correspond to (product-wise) separable functions and not every function is a linear combination of separable functions.

Oct 3, 2016 · What I can say is that the second way is very useful, because it allows us to translate an endomorphism in terms of something structurally and algebraically rich such as …

It doesn't seem to follow that $\sigma$ is a universal object in the first sense. So intuitively, it seems that "the set of the first universal objects contains the set of the second universal …

Mar 13, 2014 · The tensor product of two vector spaces is not a quotient of the Cartesian product of those spaces. It is a quotient of the free vector space with basis the cartesian product.

Apr 16, 2014 · One would use that in the sense of \sum for addition. In math sometimes you have to specify over which ring one does the tensor product (of just two modules).