Linear Algebra Done Right · Problem 7B.3

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · spectral-theorem

Problem

Suppose

\mathbf{F} = \mathbf{C}

and

T \in \mathcal{L}(V)

is normal. Prove that the set of eigenvalues of

T

is contained in

\{0, 1\}

if and only if there is a subspace

U

V

such that

T = P_U