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Let W be a vector space with inner product (,) and the norm ||x|| = √(x,x). Prove that, for u, w EW, ||u+ w||2² + ||u − w||² = 2||u||² + 2||w||2.

Let W be a vector space with inner product (,) and the norm ||x|| = √(x,x). Prove that, for u, w EW, ||u+ w||2² + ||u − w||² = 2||u||² + 2||w||2.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 24CM
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Let W be a vector space with inner product (,) and the norm ||x|| = √(x,x). Prove that, for u, w EW, ||u+ w||2² + ||u − w||² = 2||u||² + 2||w||2.
Transcribed Image Text:Let W be a vector space with inner product (,) and the norm ||x|| = √(x,x). Prove that, for u, w EW, ||u+ w||2² + ||u − w||² = 2||u||² + 2||w||2.
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