(a) Prove the identity (u.v> = 1/4(||u +v||2 - ||u - v||2), (3.11) which allows one to...

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(a) Prove the identity
(u.v> = 1/4(||u +v||2 - ||u - v||2), (3.11)
which allows one to reconstruct an inner product from its norm.
(b) Use (3.11) to find the inner product on R2 corresponding to the norm
||v|| = √u21 - 3v1v2 + 5v22.

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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 08:35 AM

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(a) Prove the identity (u.v> = 1/4(||u +v||2 - ||u - v||2), (3.11) which allows one to...

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Applied Linear Algebra

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