Linear Algebra Done Right · Problem 8A.8

Operators on Complex Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · range-powers

Problem

Suppose T∈L(V)T \in \mathcal{L}(V). Prove that range⁡Tdim⁡V=range⁡Tdim⁡V+1=range⁡Tdim⁡V+2=⋯ .\operatorname{range} T^{\dim V} = \operatorname{range} T^{\dim V + 1} = \operatorname{range} T^{\dim V + 2} = \cdots.

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