Answered: (a) Show that in an inner product…

(a) Show that in an inner product space, xly if and only if we have ||x+ay||= ||x- ay|| for all scalars a. (b) Show that in an inner product space, x1y if and only if |x+ay||2||x|| for all scalars a.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.5: Subspaces, Basis, Dimension, And Rank

Problem 10EQ

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Question

(a) Show that in an inner product space, x ly if and only if we have
||x+ ay|| = ||x- ay|| for all scalars a.
(b) Show that in an inner product space, xly if and only if |x+ay||2||x||
for all scalars a.

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