Timeline for What is the "positive part" of the unit ball in $M_n(R)$ ?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| May 22, 2020 at 17:24 | comment | added | LSpice | @LaurentBerger's reference: Sanyal, Sottile, and Sturmfels - Orbitopes. | |
| Nov 10, 2016 at 5:06 | comment | added | YCor | A few basic remarks: (a) the set of extremal points of the convex hull of $SO_n$ is exactly $SO_n$ (idem for $O^-_n$); (b) for $n$ even these sets are symmetric; (c) for all $n\ge 2$ the convex hull of $SO_n$ and $O^-_n$ have 0 in their intersection, as we see looking just at the convex hull of diagonal $\pm 1$-matrices (d) for $n\ge 3$ the convex hull of $SO_n$ and $O^-_n$ have nonempty interior (hence their intersection is a neighborhood of 0). (This is because it contains 0 and using [I skip details] that the representation in $\mathbf{R}^n$ is absolutely irreducible for $n\ge 3$.) | |
| Nov 10, 2016 at 4:33 | history | edited | YCor |
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| Nov 9, 2016 at 17:33 | vote | accept | Denis Serre | ||
| Nov 9, 2016 at 15:58 | answer | added | Suvrit | timeline score: 11 | |
| Feb 29, 2012 at 15:47 | comment | added | Denis Serre | Merci, Laurent ! | |
| Feb 29, 2012 at 15:31 | comment | added | Laurent Berger | The answer for $n=3$ is given in $\S 4.1$ of arxiv.org/abs/0911.5436. In $\S 4.4$ of ibid, there's a discussion of some properties of the convex hull of $SO(n)$ for larger $n$. | |
| Feb 29, 2012 at 9:02 | history | edited | Denis Serre | CC BY-SA 3.0 |
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| Feb 29, 2012 at 8:47 | history | edited | Denis Serre | CC BY-SA 3.0 |
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| Feb 29, 2012 at 8:44 | comment | added | Yemon Choi | Ricky, it is customary in many places/books/texts/whatever in analysis to use the word "contraction" to mean "distance non-increasing". This is how almost all practising operator theorists and most functional analysts I've met use the word, for instance | |
| Feb 29, 2012 at 8:44 | comment | added | user5810 | If $B$ is open, then $B$ has no extremal points, and so is not the convex hull of the set of its extremal points. $\hspace{.2 in}$ If $B$ is closed, then $B$ has members that are not contractions. $\;\;$ | |
| Feb 29, 2012 at 8:20 | history | asked | Denis Serre | CC BY-SA 3.0 |