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Mathematics
Linear and Abstract Algebra
Proof of Existence of Tensor Product .... Further Question ...
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[QUOTE="WWGD, post: 5414140, member: 69719"] I think a helpful thing to know/understand is the concept of maps factoring through (the quotient, here): [URL]https://en.wikipedia.org/wiki/List_of_mathematical_jargon[/URL] in algebra, there are conditions on the kernel of a map. Factoring through is in analogy with the factoring of numbers as products. You are given functions f:A-->C , g: A-->B . Then f factors through g if there is an h: with f=hg ; h is a map from B-->C. This is I think the clearest way of understanding the tensor product. For vector spaces V,W , the tensor product , ## V \ Oline W ## is a vector space in which every bilinear map defined on VxW into a third vector space Z factors through a linear map from the tensor product into Z. The conditions on the kernel guarantee that maps factor through. I will look up the conditions on the kernel and image of the respective groups and get back with it. [/QUOTE]
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Linear and Abstract Algebra
Proof of Existence of Tensor Product .... Further Question ...
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