Timeline for integer matrices with non-real spectra
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 13, 2017 at 8:41 | comment | added | Vincent | @IlyaBogdanov Ah thank you! I missed the $\det(A) = \det(B) = 1$ condition. It all makes sense now. | |
| Oct 13, 2017 at 7:56 | comment | added | Ilya Bogdanov | @Vincent: IAs for your second question --- no, I do not know how to assume that. | |
| Oct 13, 2017 at 7:55 | comment | added | Ilya Bogdanov | @Vincent: We know that $\lambda_3=\overline{\lambda_2}$, so the relation holds for it. Next, $\lambda_1\lambda_2\lambda_3=1=\mu_1\mu_2\mu_3$, whence the relation for $\lambda_1$. (I could use the basic Galois theory technique, but I needed the fixed correspondence between the roots.) | |
| Oct 13, 2017 at 7:31 | comment | added | Vincent | Perhaps a stupid question, but how do you go from $\lambda_2^k = \mu_2^l$ to $\lambda_1^k = \mu_1^l$ in the last line? Can we somehow assume wlog that $\lambda_1 = \mu_1 = 1?$ | |
| Sep 24, 2017 at 5:31 | comment | added | Misha | Thank you, Ilya! I was hoping for a positive answer, but alas... | |
| Sep 24, 2017 at 5:29 | vote | accept | Misha | ||
| Sep 23, 2017 at 19:13 | history | answered | Ilya Bogdanov | CC BY-SA 3.0 |