Timeline for Proving "almost all matrices over C are diagonalizable".
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 7, 2019 at 18:16 | comment | added | Federico Poloni | This argument only shows that the set of diagonalizable matrices is dense. | |
| Feb 2, 2010 at 23:36 | comment | added | Anweshi | @Hanche. That is Sard's theorem. | |
| Jan 24, 2010 at 16:34 | comment | added | Harald Hanche-Olsen | You're right, my argument really only proves that the set of non-diagonalizable matrices has empty interior. As a closed set with empty interior can still have positive measure, this doesn't quite clinch the argument in the measure-theoretic sense. | |
| Jan 24, 2010 at 1:31 | comment | added | Anweshi | @Harald. It perturbs me that I cannot complete this argument rigorously. Will you be able to help? | |
| Jan 24, 2010 at 0:32 | comment | added | Anweshi | The added benefit is that the same argument proves that Zariski closed sets are of measure zero. Of course, I do not know how to write it in detail with the epsilons and deltas, but I am convinced by the heuristics. I am almost tempted to accept this answer over the others! | |
| Jan 23, 2010 at 1:26 | history | edited | Harald Hanche-Olsen | CC BY-SA 2.5 |
Incorporated suggestion from the comments
|
| Jan 22, 2010 at 23:15 | comment | added | gowers | Or you could simply upper-triangularize your matrix and do the same. | |
| Jan 22, 2010 at 18:52 | history | answered | Harald Hanche-Olsen | CC BY-SA 2.5 |