Linear Algebra Done Right · Problem 8A.22

Operators on Complex Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · nilpotent-operators

Problem

Suppose T∈L(C5)T \in \mathcal{L}(\mathbf{C}^5) is such that range⁡T4≠range⁡T5\operatorname{range} T^4 \neq \operatorname{range} T^5. Prove that TT is nilpotent.

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