Timeline for Awfully sophisticated proof for simple facts
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Feb 8, 2023 at 7:02 | comment | added | Nate Eldredge | I recently stumbled on another "nuke" proof of Perron-Frobenius. Let's do the case where the matrix $A$ is stochastic. Fix a Banach limit (!!!), $\Phi \in (\ell^\infty)^*$. Apply $\Phi$ element-wise to the sequence of (stochastic) matrices $A, A^2, A^3, \dots$, and let $B$ be the $\Phi$-limit. By the linearity and positivity of $\Phi$, $B$ is stochastic. By the linearity and shift invariance, $BA=B$. So each row of $B$ is a non-negative eigenvector of the eigenvalue 1. | |
| Oct 17, 2010 at 22:46 | history | edited | JBL | CC BY-SA 2.5 |
added 1 characters in body
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| Oct 17, 2010 at 21:41 | comment | added | Tom Smith | "Flamed", not "fired"! | |
| Oct 17, 2010 at 20:07 | comment | added | Denis Serre | I mean that someone wrote a nasty review because of that. | |
| Oct 17, 2010 at 19:36 | comment | added | The Mathemagician | And they fired you for this? OoOoOo,they would have been SO sued... | |
| Oct 17, 2010 at 19:07 | history | answered | Denis Serre | CC BY-SA 2.5 |