Linear Algebra Done Right · Problem 7A.13

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · self-adjoint-operators

Problem

Suppose

\mathbf{F} = \mathbf{R}

. Define

\mathcal{A} \in \mathcal{L}(\mathcal{L}(V))

\mathcal{A}T = T^*

for all

T \in \mathcal{L}(V)

. (a) Find all eigenvalues of

\mathcal{A}

. (b) Find the minimal polynomial of

\mathcal{A}