Timeline for Inverting a linear system of inequalities
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 24, 2023 at 15:30 | comment | added | Dirk | It's more complicated than what you state (just consider $A=-I$ to see that the bounds can not be like you want them in your initial statement). | |
| Feb 24, 2023 at 14:43 | comment | added | Iosif Pinelis | Also, looking at your $f(l) \le x \le g(r)$, it seems that you want the lower bound on $x$ to depend only on $l$, and the upper bound on $x$ to depend only on $r$. On the other hand, in your "Concrete example", these "depend only on" conditions do not seem to hold. ?? | |
| Feb 24, 2023 at 14:32 | comment | added | Iosif Pinelis | In "When can we invert this system?", what do you mean by "when"? Do you want a necessary and sufficient condition? If so, in what terms do you want the condition on $A,l,r$ to be stated? | |
| Feb 24, 2023 at 13:02 | comment | added | Carlo Beenakker | but you want not just any linear transformation, but an orthogonal transformation, right? that will not work in general. | |
| Feb 24, 2023 at 12:22 | comment | added | AspiringMat | @CarloBeenakker This doesn't rule out that a linear transormation would give such set right? For example, setting $r=m'+z', s=z'+p', t=..$ leading to such set. | |
| Feb 24, 2023 at 11:52 | comment | added | Carlo Beenakker | I don't think this is possible: the bounds on $m'$ will depend on $z'$ and $p'$, so you can not hope to obtain an equality of the form $f(m,z,p)\leq m'\leq g(m,z,p)$. | |
| Feb 24, 2023 at 11:28 | history | asked | AspiringMat | CC BY-SA 4.0 |