Linear Algebra Done Right · Problem 7A.15

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · self-adjoint-operators

Problem

Suppose T∈L(V)T \in \mathcal{L}(V) is invertible. Prove that (a) TT is self-adjoint   ⟺  \iff T−1T^{-1} is self-adjoint; (b) TT is normal   ⟺  \iff T−1T^{-1} is normal.

Related theory

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