Suppose that g(z)=f(x), where x=Sz+s for some S\in R^{n\times n} and s\in R^n

Please Show that \nabla g(z)=S^T\nabla f(x) and \nabla^2g(z)=S^T\nabla^2 f(x) S

where \nabla shows the gradient and \nabla^2 shows the Hessian.

Hessian of a vector is defined by:


Any help would be sincerely appreciated.