Answered: 2. If S = {v₁,...,Un} is an orthonormal…

2. If S = {v₁,...,Un} is an orthonormal set in an inner product space V, prove that for any x EV n Σ(x, v₁) ≤ ||x|| ². i=1

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 17E: If e is the unity in an integral domain D, prove that (e)a=a for all aD. [Type here][Type here]

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Question

12. Show all the steps clearly please

12. If S = {v₁,..., Un} is an orthonormal set in an inner product space V, prove that for
any x EV
N
Σ(x, vi) ≤ ||x|| ².
i=1

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