E = {u: [0, 7] → Rª | u is absolutely continuous,le (0) = u(T), ù ≤ L²([0, 7]. R^)}with the inner product[*[(i(1), v (1)) + (u(1), v(1))]drfor all u, v € E where (...) denotes the inner product in RN. The corresponding normis defined by[*(\à(1³² +\u(1)³²)dt. V u € E.< u,v>E=||u|| E =For every u, ve E, we defineeQ(¹) [(ù (1), v(1)) + (A(1)u(1), v(1))]dt,and we observe that, by the assumptions (A1) and (A2), it defines an inner product inE. Then, E is a separable and reflexive Banach space with the norm||u|| =< u, u > ²4. V Y=Vue E.||ul|∞ ≤S||u||where ||ul|∞ = max;c[0,71 |u(1)|.The question is why is normdefined in this way, please clarify?(2)

An inner product space is a real vector space or a complex vector space with an operation called an…

Answered: E = {u: [0, 7] → Rª | u is absolutely…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 12EQ

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