Timeline for geometric intuition for A and A-transpose having the same eigenvalues
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 25, 2020 at 20:42 | vote | accept | soupy | ||
| Aug 30, 2017 at 8:03 | comment | added | Federico Poloni | Note that, in a generalization of this argument to a non-diagonalizable matrix, if $v_1$ is an eigenvector and $v_2$ is the second vector of a Jordan basis, then their duals swap their roles: $f_2$ is the eigenvector and $f_1$ is the generalized eigenvector. I think that the generalized proof will have to account for this property in some way. | |
| Jul 30, 2017 at 23:16 | comment | added | Ted Shifrin | Since you need the eigenvalue in there, I don't quite see it quickly, @Qiaochu. | |
| Jul 30, 2017 at 23:02 | comment | added | Qiaochu Yuan | You can run basically the same argument with the expression $(A - I)^k$ and generalized eigenvectors. | |
| Jul 30, 2017 at 22:54 | comment | added | Ted Shifrin | What if there is no eigenbasis? | |
| Jul 30, 2017 at 22:18 | history | answered | Qiaochu Yuan | CC BY-SA 3.0 |