Assume $T$ is a normal operator on the complex finite dimensional inner product space $(V,\langle\,\cdot ,\,\cdot\rangle)$. Prove that $Range(T^k)=Range(T)$ and $Ker(T^k)=Ker(T)$ for all natural numbers k.
normal operator proof question on complex space
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linear-algebra
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0First try showing these statements to be true assuming that $T$ is diagonal. – 2012-12-01