Linear Algebra Done Right · Problem 7B.2

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · spectral-theorem

Problem

Suppose

\mathbf{F} = \mathbf{C}

. Suppose

T \in \mathcal{L}(V)

is normal and has only one eigenvalue. Prove that

T

is a scalar multiple of the identity operator.