Linear Algebra Done Right · Problem 7A.6

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · adjoints

Problem

Suppose T∈L(V,W)T \in \mathcal{L}(V, W). Prove that (a) TT is injective   ⟺  \iff T∗T^* is surjective; (b) TT is surjective   ⟺  \iff T∗T^* is injective.

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