Linear Algebra Done Right · Problem 7B.21

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · spectral-theorem

Problem

Suppose that

T

is a self-adjoint operator on a finite-dimensional inner product space and that 2 and 3 are the only eigenvalues of

T

. Prove that

T^2 - 5T + 6I = 0.