Linear Algebra Done Right · Problem 6A.6

Inner Product Spaces — Sheldon Axler

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

Problem

Suppose

u, v \in V

. Prove that

\langle u, v \rangle = 0 \iff \|u\| \leq \|u + av\|

for all

a \in \mathbf{F}