Linear Algebra Done Right · Problem 7D.6

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · isometries-unitary-operators

Problem

Suppose

T_1, T_2

are both normal operators on

\mathbf{F}^3

with

2, 5, 7

as eigenvalues. Prove that there exists a unitary operator

S \in \mathcal{L}(\mathbf{F}^3)

such that

T_1 = S^* T_2 S