Linear Algebra Done Right · Problem 7D.12

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · isometries-unitary-operators

Problem

Prove or give a counterexample: If

S \in \mathcal{L}(V)

is invertible and

\|S^{-1}v\| = \|Sv\|

for every

v \in V

, then

S

is unitary.