I need to demonstrate the previous.
What i said is... ...symmetrical endomorphism operator with all the eigenvalues positive means that he represents an "expansion" of the space $W$. this means that if i write every vector $v$ as:
$$v=\lambda_1 e_1 + \lambda_2 e_2 +...+\lambda_n e_n$$
with $e_1,...e_n$ indipendent vectors from the autospaces of $f$. Then $f(v)$ will be like:
But sign of $(e_i,e_i)$ will be $(+,+)$ or $(-,-)$
(because i said that $f$ is an "expansion" of the space $W$!) and $\Lambda_i$ will be all positive numbers!
So the euclidean scalar product of $\Omega(f(v),v)$ will be always $>0$ (if $v$ is different form $0$).
Im wrong? If yes, why?