Let $f:\mathbb{R}^2 \to \mathbb{R}$ be twice continuously differentiable and $L: \mathbb{R}^2 \to \mathbb{R}^2$ be linear described by the matrix $A \in \mathbb{R}^{2 \times 2}$. Let $g: \mathbb{R}^2 \to \mathbb{R}, \ g(x,y) = f(L(x,y))$.
What relation do $H_f(0)$ and $H_g(0)$ share? (These $H$'s are Hessian matrices.)
By mere calculation, I can't seem to find any algebraic relationship. Perhaps, it is asked about size properties or linear algebra properties?