Linear Algebra Done Right · Problem 7A.28

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · normal-operators

Problem

Suppose

T \in \mathcal{L}(V)

is normal. Prove that if

\lambda \in \mathbf{F}

, then the minimal polynomial of

T

is not a polynomial multiple of

(x - \lambda)^2