Timeline for Is there any meaningful extension of the notion of a vector space for multisets?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Jun 19, 2018 at 17:46 | vote | accept | aghostinthefigures | ||
| Jun 19, 2018 at 12:35 | answer | added | Gro-Tsen | timeline score: 3 | |
| Jun 19, 2018 at 8:08 | answer | added | Aaron Meyerowitz | timeline score: 4 | |
| Jun 19, 2018 at 7:20 | history | edited | YCor |
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| Jun 19, 2018 at 3:53 | history | edited | aghostinthefigures | CC BY-SA 4.0 |
Clarified properties I'd like to see retained in such an extension of a vector space.
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| Jun 19, 2018 at 3:21 | history | edited | Andrés E. Caicedo |
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| Jun 19, 2018 at 0:56 | comment | added | Wlod AA | I'd need much more complete definitions. | |
| Jun 19, 2018 at 0:08 | comment | added | aghostinthefigures | Willing and able. My expectation is that a host of uniqueness theorems for these vector space analogues would fail, but other theorems would hold. Consider the Hilbert projection theorem for some Hilbert space $H$; for some multiset corresponding to a "cloned Hilbert space", the norm-minimizing element uniqueness portion of the theorem fails but the orthogonality portion holds. (If $\color{red}x$ and $\color{blue}x$ are both minimizing elements of $||x-y||$ where $y$ is in some sub"space" $C$, I expect both $\color{red}x - y$ and $\color{blue}x - y$ to be orthogonal to the elements in $C$.) | |
| Jun 19, 2018 at 0:05 | answer | added | Bjørn Kjos-Hanssen | timeline score: 1 | |
| Jun 18, 2018 at 23:49 | comment | added | Gerhard Paseman | How willing are you to give up uniqueness? Gerhard "One Won't Be Loneliest Number" Paseman, 2018.06.18. | |
| Jun 18, 2018 at 21:04 | review | First posts | |||
| Jun 18, 2018 at 21:20 | |||||
| Jun 18, 2018 at 21:02 | history | asked | aghostinthefigures | CC BY-SA 4.0 |