E =ue (0) =with the inner product{u: [0, 7] → RN | u is absolutely continuous,u(T), ù € L²([0, 7]. RN)}[[(i(1), v (1)) + (u(1), v(1))]drfor all u, v € E where (...) denotes the inner product in RN. The corresponding normis defined byAU. VYTE=||u||E= [(lù(1³² +\u(1)1³²)dr. V u € E.For every u, ve E, we define=S² eQ(¹) [(ù (1), v(1)) + (A(1)u(1), v(t))]dt,4. V Y=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 > ²Vue E.||ul|∞ ≤S||u||where ||ul|∞ = maxic[0,71 |u(t)].The question is why is normdefined in this way, please clarify?(2)

Given as, E={u:o,T→ℝn u is absolutely continuous. u(0)=u(T).u∈L2o,T,,ℝN}˙ the inner product…

Answered: oduct AU. VYE= where (, ) de

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 25CM: Find a basis B for R3 such that the matrix for the linear transformation T:R3R3,...

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