Linear Algebra Done Right · Problem 6A.7

Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · inner-products-and-norms

Problem

Suppose

u, v \in V

. Prove that

\|au + bv\| = \|bu + av\|

for all

a, b \in \mathbf{R}

if and only if

\|u\| = \|v\|