Answered: Suppose p > 0. Prove that there is an…

Suppose p > 0. Prove that there is an inner product on R2 such that the associated norm is given by ||(x, y)|| = (xP + yP)'/P for all (x, y) e R² if and only if p = 2.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Suppose p > 0. Prove that there is an inner product on R2 such that the
associated norm is given by
||(x, y)|| = (xP + yP)'/P
for all (x, y) e R² if and only if p = 2.

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