Timeline for Image of a quadratic form is a closed cone
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Sep 12, 2022 at 11:54 | comment | added | Jochen Glueck | Today I happened to find a simple counterexample which shows that $Q(E)$ is not always convex: let $E = \mathbb{R}^2$ and $F = \mathbb{R}^{2 \times 2}$, and let $B(x,y) = xy^{\operatorname{T}}$ for all $x,y \in E$. Then the range of $Q$ is the set of the symmetric matrices of rank $\le 1$, which is not convex. | |
| Jun 2, 2022 at 20:38 | comment | added | Jochen Glueck | Thanks for your response! | |
| Jun 2, 2022 at 20:32 | comment | added | Eduardo Longa | I didn't found out :( but I suspect it may not be always convex | |
| May 26, 2022 at 17:28 | comment | added | Jochen Glueck | May I ask whether you found out whether $Q(E)$ is always convex? | |
| May 25, 2022 at 6:24 | history | became hot network question | |||
| May 25, 2022 at 1:22 | vote | accept | Eduardo Longa | ||
| May 25, 2022 at 0:16 | answer | added | Jochen Glueck | timeline score: 7 | |
| May 25, 2022 at 0:11 | comment | added | Jochen Glueck | I'll post a counterexample. But in fact, I'm quite confused about the convexity now. (Probably because I should actually sleep rather than doing maths...) | |
| May 25, 2022 at 0:09 | history | edited | Eduardo Longa |
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| May 25, 2022 at 0:08 | comment | added | Eduardo Longa | Really? Do you have a counterexample in mind? What if the norms are induced by an inner product? | |
| May 24, 2022 at 22:40 | history | edited | Eduardo Longa | CC BY-SA 4.0 |
added 45 characters in body; edited title
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| May 24, 2022 at 22:24 | history | asked | Eduardo Longa | CC BY-SA 4.0 |