please read it completely i need perfect answer Suppose that V is an inner product space, T: V → V is a linear operator, and that for all v E V we have||T(v) || = ||v||Prove that T is injective.

Given: V is an inner vector space, T:V→V is a linear operator, Tv=v, v∈V.To prove: T is injective.

Answered: Suppose that V is an inner product…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.CR: Review Exercises

Problem 71CR: Let V be an inner product space. For a fixed nonzero vector v0 in V, let T:VR be the linear...

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Suppose that V is an inner product space, T: V→ V is a linear operator, and that for all v EV we have ||T(v) || = ||v|| Prove that T is injective.