Linear Algebra Done Right · Problem 7A.3

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · adjoints

Problem

Suppose

T \in \mathcal{L}(V)

and

\lambda \in \mathbf{F}

. Prove that

\lambda \text{ is an eigenvalue of } T \iff \bar{\lambda} \text{ is an eigenvalue of } T^*.