Ivan Shishkin, Rye (1878)

Problems/Linear algebraExerciseUnreviewed

Valeurs propres d’une matrice nilpotente

by Sequoia·
25
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 AA une matrice nilpotente de taille nn et d’indice de nilpotence pp.
Soit λ∈C\lambda\in\mathbb{C} un complexe λ\lambda tel qu’il existe un vecteur X≠0X\neq0 tel que AX=λXAX=\lambda X.

Calculer ApXA^pX de deux manières. En déduire que λ=0\lambda=0.

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