Linear Algebra Done Right · Problem 7B.8

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · spectral-theorem

Problem

Suppose

\mathbf{F} = \mathbf{C}

and

T \in \mathcal{L}(V)

. Prove that

T

is normal if and only if every eigenvector of

T

is also an eigenvector of

T^*