Timeline for Left and right eigenvectors are not orthogonal
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Nov 18, 2022 at 7:35 | vote | accept | Guido Li | ||
| Nov 17, 2022 at 19:01 | history | edited | Jochen Glueck | CC BY-SA 4.0 |
added 3 characters in body
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| Nov 17, 2022 at 18:53 | comment | added | Willie Wong | Thank you very much for the expanded discussion, and for pointing out your PhD Thesis with its very useful appendix. | |
| Nov 17, 2022 at 18:27 | comment | added | Jochen Glueck | By the way, I'd suspect more generally that the following statements are equivalent for any pole $\lambda$ of the resolvent of a linear operator: (i) The eigenvalue $\lambda$ is semi-simple; (ii) The eigenspace of $\lambda$ separates the dual eigenspace; (iii) the dual eigenspace separates the eigenspace; (iv) the eigenspace and the dual eigenspace separate each other. But admittedly, I haven't thought about it in too much detail, yet, so currently I'm not completely sure whether this characterization is indeed correct. | |
| Nov 17, 2022 at 18:22 | comment | added | Jochen Glueck | @GuidoLi: Thanks for your response. I've now added various details. | |
| Nov 17, 2022 at 18:22 | comment | added | Jochen Glueck | @WillieWong: Sorry for the delay. I've added many details, and discussed a few references in the end. I hope it's easier to follow the argument now. | |
| Nov 17, 2022 at 18:21 | history | edited | Jochen Glueck | CC BY-SA 4.0 |
I added a lot of details to the answer.
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| Nov 16, 2022 at 23:41 | comment | added | Guido Li | @JochenGlueck thanks jochen for your answer, I admit i would also like to hear a bit more about why the projections what you call 'separate' each other... | |
| Nov 16, 2022 at 17:31 | comment | added | Jochen Glueck | @WillieWong: Sorry for the confusion! I'm on a bus right now (with just my mobile phone and no books), but I'll add some references and explanations later. | |
| Nov 16, 2022 at 17:30 | comment | added | Jochen Glueck | @GiorgioMetafune: Yes, in the sense that Willie Wong mentions. | |
| Nov 16, 2022 at 17:27 | comment | added | Willie Wong | I find myself too poorly educated to understand how any single sentence in the proof goes. Do you have a reference that I can look at for this? | |
| Nov 16, 2022 at 17:21 | comment | added | Willie Wong | I think (but not sure) it means given any $v \neq w$ in $\ker(\lambda - T)$ you can find $x$ in $\ker(\bar{\lambda} - T^*)$ such that $x(v)\neq x(w)$; and vice versa. @GiorgioMetafune | |
| Nov 16, 2022 at 17:16 | comment | added | Giorgio Metafune | What you mean by "separate each other"? | |
| Nov 16, 2022 at 16:59 | history | answered | Jochen Glueck | CC BY-SA 4.0 |