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Theorem 9.6.1. Let V be a real vector space. A norm ||· || is induced by an inner product if and only if, for all x, y € V, the norm satisfies ||x + y||² + ||x − y||² = 2||x||² +2||y||² (PARALLELOGRAM LAW). (9.1) AFT

Theorem 9.6.1. Let V be a real vector space. A norm ||· || is induced by an inner product if and only if, for all x, y € V, the norm satisfies ||x + y||² + ||x − y||² = 2||x||² +2||y||² (PARALLELOGRAM LAW). (9.1) AFT

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 44E: Prove that in a given vector space V, the additive inverse of a vector is unique.
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Theorem 9.6.1. Let V be a real vector space. A norm || || is induced by an inner product if and only if, for all x, y € V, the norm satisfies ||x + y||² + ||x − y||² = 2||×||² +2||y||² (PARALLELOGRAM LAW). (9.1) AFT
Transcribed Image Text:Theorem 9.6.1. Let V be a real vector space. A norm || || is induced by an inner product if and only if, for all x, y € V, the norm satisfies ||x + y||² + ||x − y||² = 2||×||² +2||y||² (PARALLELOGRAM LAW). (9.1) AFT
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