Linear Algebra Done Right · Problem 7E.16

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · singular-value-decomposition

Problem

Suppose

T \in \mathcal{L}(V, W)

. Prove that

(T^*)^\dagger = (T^\dagger)^*

. Compare the result in this exercise to the analogous result for invertible linear maps [see 7.5(f)].