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 May 9th, 2014, 12:07 AM #1 Newbie   Joined: Nov 2013 Posts: 26 Thanks: 0 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?
 May 9th, 2014, 03:54 AM #2 Senior Member   Joined: Dec 2013 From: Russia Posts: 327 Thanks: 108 Recall that $(T^2u,u)=(Tu,Tu)$. Thanks from Deveno and Sandra93

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