Ivan Shishkin, Rye (1878)

Problems/Hilbert and pre-Hilbert spaceExercise

Norme à partir d’un produit scalaire

by 2doupi·
30
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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Soit φ\varphi un produit scalaire sur un espace vectoriel EE.
Montrer que
f:E→Rx↦φ(x,x)\begin{matrix}f:&E&\rightarrow&\R\\ & x&\mapsto&\sqrt{\varphi(x,x)}\end{matrix}est une norme.

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