Ivan Shishkin, Rye (1878)

Problems/Linear algebraUnreviewed

Endomorphismes stables

by Uettechat·
40
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
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Soit EE un K-ev\mathbb{K}\text{-ev} de dimension finie n∈N∗n\in\mathbb{N}^{*}.

  1. Quels sont les endomorphismes de EE laissant stables toutes les droites vectorielles de EE?
  2. Soit p∈{1,...,n−1}p\in\{1,...,n-1\}. Quels sont les endomorphismes de EE laissant stables tous les sev de EE de dimension pp?
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