Linear Algebra Done Right · Problem 8A.1

Operators on Complex Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · null-spaces-powers

Problem

Suppose T∈L(V)T \in \mathcal{L}(V). Prove that if dim⁡null⁡T4=8\dim \operatorname{null} T^4 = 8 and dim⁡null⁡T6=9\dim \operatorname{null} T^6 = 9, then dim⁡null⁡Tm=9\dim \operatorname{null} T^m = 9 for all integers m≥5m \geq 5.

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