Timeline for Tensor product and category theory
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Apr 7, 2015 at 8:56 | comment | added | tom | I found this characterization very helpful, thanks. The only thing is, as you mention, some elements of $U\otimes V$, like $x_1\otimes y_1 + x_2\otimes y_2$, don't correspond directly to things you can plug into a bilinear map. So perhaps the elements of $U\otimes V$ are the things you can build from the things you can plug into a bilinear map, using definitions of addition and scalar multiplication on these objects consistent with bilinearity? :D | |
| Jul 17, 2010 at 21:30 | comment | added | David Corwin | Right, I'm thinking about finite-dimensional spaces. In the infinite dimensional case, it still gives some of them. | |
| Jul 16, 2010 at 8:39 | comment | added | Yemon Choi | Does (dual of V) $\otimes$ (dual of V) give all the bilinear forms on $V$ when $V$ is infinite-dimensional? Certainly if one starts wanting to put norms on such spaces (when using continuous duals), care is needed. | |
| Jul 15, 2010 at 16:06 | history | edited | David Corwin | CC BY-SA 2.5 |
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| Jul 15, 2010 at 11:28 | vote | accept | Dedalus | ||
| Jul 15, 2010 at 10:17 | history | answered | David Corwin | CC BY-SA 2.5 |