Let V be a normed vector space. Prove that a linear map L: V V defines

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Let V be a normed vector space. Prove that a linear map L: V → V defines an isometry of V for the given norm if and only if it maps the unit sphere S1 = {||u|| = 1} to itself:
L[S1] = {L[u] | u ∈ S1} = S1.

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Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

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Question Posted: Jun 17, 2016 09:01 AM

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Let V be a normed vector space. Prove that a linear map L: V V defines

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First if L is an isometry and u 1 then Lu ...View the full answer

Applied Linear Algebra

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