Timeline for Positive matrices matrices over commutative rings
Current License: CC BY-SA 3.0
9 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jun 5, 2011 at 9:13 | vote | accept | Joakim Arnlind | ||
| Jun 5, 2011 at 9:13 | vote | accept | Joakim Arnlind | ||
| Jun 5, 2011 at 9:13 | |||||
| Jun 1, 2011 at 7:56 | comment | added | Stefan Waldmann | Dear Joakim, the kind of examples which I have studied a lot are $^*$-algebras over a ring $C = R(i)$ with an ordered ring $R$ in the sense above. For those, you can actually say a lot. And if I'm not completely mistaken, then in the commutative case one might be able to show the positivity of $\mathrm{tr}(AB)$ for positive $A, B$ in this type of examples: maybe even for both canonical positive cones, the sum of square cone and the one defined by positive functionals, which is slightly larger. I will have to think about it... | |
| May 31, 2011 at 21:54 | comment | added | Joakim Arnlind | Thanks for the references and the examples Stefan! I have already look them up. Coming back to example no 3 above: I certainly want to have a setup that includes the case of smooth functions on a manifold. Can one find a nice class of rings / algebras (including algebras of smooth functions on a manifold) for which "theorems about positive matrices" hold? What is the crucial property that one needs? Maybe it is technically easier to stick to a positivity defined through positive functionals? | |
| May 31, 2011 at 9:33 | history | edited | Stefan Waldmann | CC BY-SA 3.0 |
added 1847 characters in body
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| May 31, 2011 at 8:49 | comment | added | Stefan Waldmann | @darij: yeah, I was too fast. Sorry. So with zero divisors, I believe that this will cause problems indeed. One may have to take a look to the particular situation. :( | |
| May 31, 2011 at 8:43 | comment | added | darij grinberg | According to his comments, his situation is more general (too general, maybe). | |
| May 31, 2011 at 8:37 | history | answered | Stefan Waldmann | CC BY-SA 3.0 |