Timeline for On Polynomial Characterization of Projection area of semidefinite matrices
Current License: CC BY-SA 3.0
10 events
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| Sep 19, 2017 at 1:08 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 20, 2017 at 1:00 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jul 21, 2017 at 0:04 | history | edited | gondolf | CC BY-SA 3.0 |
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| Jul 20, 2017 at 12:07 | comment | added | Dima Pasechnik | @gondolf I posted an answer describing the "dual" to $S$ set, for which indeed a lot is known---at least it is known whether the algebraic equation comes from. | |
| Jul 20, 2017 at 12:04 | answer | added | Dima Pasechnik | timeline score: 1 | |
| Jul 20, 2017 at 0:16 | comment | added | gondolf | @Dima Pasechnik Thank you! I am particularly interested in the case that $m=4$. Is there a clear characterization of this case? | |
| Jul 19, 2017 at 7:45 | comment | added | Dima Pasechnik | It should be easy to prove that $S$ is a semi-algebraic set in $\mathbb{R}^m$ (notice that your map, defining $S$ as the image of $D$, is linear), and the boundary of semialgebraic set is semialgebraic: en.wikipedia.org/wiki/Semialgebraic_set How exactly it can be described is a much harder question. | |
| Jul 19, 2017 at 1:47 | comment | added | Tobias Fritz | As you may already know, your $S$ is the convex hull of the joint numerical range of the $A_i$'s. The paper arxiv.org/pdf/0812.1624 may help, which is essentially concerned with the case $m=2$ (take $A=A_1 + iA_2$). | |
| Jul 19, 2017 at 0:03 | history | edited | gondolf | CC BY-SA 3.0 |
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| Jul 18, 2017 at 22:11 | history | asked | gondolf | CC BY-SA 3.0 |