Linear Algebra Done Right · Problem 7B.22

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · spectral-theorem

Problem

Give an example of an operator

T \in \mathcal{L}(\mathbf{C}^3)

such that 2 and 3 are the only eigenvalues of

T

and

T^2 - 5T + 6I \neq 0