Ivan Shishkin, Rye (1878)

Problems/Linear algebra

Matrices, exponentielle et nilpotence

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58
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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FrançaisEnglish

Soient A,B∈Mn(R)A,B \in \mathcal{M}_n(\R) et P∈R[X]P\in \R[X]. Montrer que P ⁣(eAB)P\!\left(e^{{AB}} \right) est nilpotente si et seulement si P ⁣(eBA)P\!\left(e^{{BA}} \right) est nilpotente.

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