Timeline for Generic linear subspaces of symmetric matrices
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 5, 2020 at 13:04 | comment | added | Ilya Bogdanov | There are much larger subspaces all whose elements have two equal eigenvalues --- say, the matrices where the first two rows vanish (you may also replace the $(1,1)$th and $(2,2)$th entries by two equal numbers). So the answer to the first question does nor exceed $2n-1$. | |
| Sep 5, 2020 at 6:50 | comment | added | YCor | In any case so far I only see $b(n)\ge 2$ for $n$ even and $b(n)\ge 1$ for $n$ odd. Any better lower bound? Do you know what is $b(3)\in\{1,2,3,4\}$? | |
| Sep 4, 2020 at 23:05 | comment | added | Andy Sanders | @YCor, I'm not convinced naming the integer really adds anything to question, and given your comment, it should be clear to readers. As to your second comment, the title should really include "linear subspaces all of whose elements are generic," but I couldn't figure out how to say this without sounding long-winded. | |
| Sep 4, 2020 at 22:23 | comment | added | YCor | (I'm not sure why the word "generic" is used in the question: this is not about generic subspaces.) | |
| Sep 4, 2020 at 22:21 | comment | added | YCor | It might be useful to give a name, say $b(n)$, to the integer defined by the question. The observation on intersection with $\Delta$ gives $b(n)\le n(n+1)/2-1- (n-2)$, and $b(2)=2$. | |
| Sep 4, 2020 at 20:26 | history | asked | Andy Sanders | CC BY-SA 4.0 |