Ivan Shishkin, Rye (1878)

Problems/Linear algebraReviewed

Famille de n+1n+1 vecteurs unitaires équiangles

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 (E,⟨⋅,⋅⟩)(E, \langle\cdot ,\cdot \rangle ) un espace euclidien de dimension nn. Montrer que l’on peut trouver des vecteurs x1,...,xn+1∈Ex_{1},...,x_{n+1} \in E unitaires tels que ∀i≠j,⟨xi,xj⟩=−1/n\forall i \neq j, \langle x_{i},x_{j} \rangle=-1/n.

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