Ivan Shishkin, Rye (1878)

Problems/Linear algebraUnreviewed

A family of n+1n+1 equiangular unit vectors

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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
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  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
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Let (E,⟨⋅,⋅⟩)(E,\langle\cdot, \cdot\rangle) be a Euclidean spaceFR of dimension nn. Show that there exist unit vectors x1,…,xn+1∈Ex_1, \ldots, x_{n+1} \in E such that ⟨xi,xj⟩=−1/n\langle x_i, x_j\rangle=-1/n for all i≠ji \neq j.

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