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May 9th, 2014, 12:07 AM   #1
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self-adjoint operator

Hi,

T is a self-adjoint Operator on a vector space V. I have to Show that:

$\displaystyle T^2=0 \Rightarrow T=0$


... my first idea was to argue with the Eigenvalues, because if $\displaystyle \lambda $ is Eigenvalue of T then $\displaystyle \lambda^2$ is Eigenvalue of $\displaystyle T^2$

is that a possible way, because it seams a little bit weak... or is there a better way to prove it?
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May 9th, 2014, 03:54 AM   #2
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Recall that $(T^2u,u)=(Tu,Tu)$.
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