Timeline for Left and right eigenvectors are not orthogonal
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Nov 18, 2022 at 7:35 | vote | accept | Guido Li | ||
| Nov 16, 2022 at 16:59 | answer | added | Jochen Glueck | timeline score: 5 | |
| Nov 16, 2022 at 16:15 | comment | added | Guido Li | @CarloBeenakker indeed, but observe they are finite-dimensional arguments. | |
| Nov 16, 2022 at 15:49 | comment | added | David E Speyer | This ought to be true because, in the finite dimensional case, if $\lambda \neq \mu$, then the generalized left $\lambda$-eigenspace is orthogonal to the right generalized $\mu$-eigenspace. So, if we were to impose in addition that $\lambda$ be algebraically simple and that the left $\lambda$-eigenspace is orthogonal to the right $\lambda$-eigenspace, then the the left $\lambda$-eigenspace is orthogonal to everything, contradiction. Not posting this as an answer because I never feel confident in the infinite dimensional world. | |
| Nov 16, 2022 at 15:47 | comment | added | Carlo Beenakker | several proofs are at math.stackexchange.com/q/794520/87355 | |
| Nov 16, 2022 at 15:36 | history | edited | Guido Li | CC BY-SA 4.0 |
added 14 characters in body
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| Nov 16, 2022 at 15:35 | comment | added | Guido Li | algebraically simple, yes! | |
| Nov 16, 2022 at 10:08 | comment | added | Jochen Glueck | Do I assume correctly that by "simple", you mean algebraically simple (rather than only geometrically simple)? | |
| Nov 16, 2022 at 9:20 | history | asked | Guido Li | CC BY-SA 4.0 |