Ivan Shishkin, Rye (1878)

Problems/Differential equation

Une formule (presque) générale pour le produit de deux exponentielles

by NawzadHogan·
45
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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ReviewedReviewed by Ancient Tree
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Soient A,B∈Mn(R)A,B\in M_{n}(\R) telles que AA et BB commutent avec [A,B]:=AB−BA[A,B]:=AB-BA, leur crochet de Lie. Montrer que :
exp⁡(A)exp⁡(B)=exp⁡(A+B+12[A,B]).\exp(A)\exp(B)=\exp\left(A+B+\frac{1}{2}[A,B]\right).

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