polynome annulateur

nic1 · April 2006

Bonjour,

il est écrit dans un message sur ce site que pout tout endo. $u$ de polynome minimal $m$, il existe un vecteur $x$ de $E$ tel que le polynôme minimal de $x$ soit égale à $m$.

quelqu'un pourrait-il préciser?

taupin20 · April 2006

Pour x dans E, l'ensemble des polynômes P tels que (P(u))(x)=0 est un idéal. Si dim E <oo, il existe x tel que cet idéal soit égal à l'idéal annulateur de u. Nous avons fait cela en exo, mais c'est assez long. Si le corps de base K est infini, la preuve se simplifie.

nic1 · April 2006

et même dans le cas ou K est infini?

oumpapah0 · April 2006

Bonjour
 
 j'ai donné une demo sur ce site le 11/09/2004 à 15h 18'
 
 faire une recherche " polynomes d'endomorphismes" Oumpapah
 
 Oump.
 [Voici le message en question. AD]
 <a href = "http://www.les-mathematiques.net/phorum/read.php?f=2&i=111771&t=111448#reply_111771"> http://www.les-mathematiques.net/phorum/read.php?f=2&i=111771&t=111448#reply_111771 </a>

nic1 · April 2006

merci......

Nick5 · May 2006

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polynome annulateur

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Bonjour!

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