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 th...

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 them, without …

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-direct …

Sep 22, 2022 · Can a tensor be defined in terms of tensor products, and if so, what else can be said? I have already gone through the following questions: What is the difference between tensors and …

Mar 24, 2025 · Exercise: show that the tensor product as defined here satisfies the same quotient relations as I outlined above. I don't think there is a "best" intuitive understanding of the tensor …

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 kind.

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 objects". Am I correct? …

Nov 15, 2020 · I tried to write derived tensor products using semantex (copied from p. 27 in the manual). \documentclass {article} \usepackage {amsmath,semantex} \NewSymbolClass\MyBinaryOperator [ …

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 the tensor product. …

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.