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Let $V$ inner product space from finite dimension under $\mathbb C$ and $T: V\to V$ linear transformation so that $$T^2=\frac{T+T^*}{2}.$$

I proved that is normal and I need also to prove that $T^2-T=0$.

I'd love your help with this.

Thanks!

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    Hint: you know that $T$ is normal, so (I presume) you know that it has an orthonormal basis of eigenvectors. Consider what properties its eigenvalues must have.2011-08-18
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    Sorry I rolled back just because I was curios to see how does it look before and after, How do I return it?2011-08-18

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