Hello,

I need to prove that $\displaystyle <F''(x)h,h>=0 \Longleftrightarrow F''(x)h=0$ where $\displaystyle F''(x)$ is the hessian matrix and therefore is PSD $\displaystyle \Longrightarrow F''(x)=R^TR$ (Cholesky).

Trying to prove the first direction I basically end with $\displaystyle h^TR^TRh=0$ but can not see why it implies that $\displaystyle R^TRh=0$

Can anyone please advice?

TIA,
Best regards,
Giovanni