Let $T$ be a self-adjoint operator in V and $A=[T]_B$ where $B$ s an orthonormal basis of $V$.
So, I have to prove that $T$ is positive definite if and only if $L_A$ is positive definite.
I haven't tried much since I don't really known where to start. I've proven that $T$ is definite positive if and only if all its eigen values are positive, but I don't know if that will help.