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

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
icon
Related questions
Question
Let W be a vector space with inner product (,) and the norm ||x|| = √(x,x).
Prove that, for u, w € W,
||u+ w||² + ||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 € W, ||u+ w||² + ||u − w||² = 2||u||² +2||w||².
Expert Solution
steps

Step by step

Solved in 3 steps with 1 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage