Linear Algebra Done Right · Problem 6A.24

Inner Product Spaces — Sheldon Axler

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

Problem

Prove or give a counterexample: If

\|\cdot\|

is the norm associated with an inner product on

\mathbf{R}^2

, then there exists

(x, y) \in \mathbf{R}^2

such that

\|(x, y)\| \neq \max\{|x|, |y|\}