Hello,

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

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

Can anyone please advice?

TIA,
Best regards,
Giovanni