I'm trying to see why the following identity is true. I've lifted it from an exercise in Miles Reid Algebraic Geometry. I'm having difficult deriving it and feel there might be a simple line or two to do it?
If $x_i'$ = $\sum a_{ij}x_j$ is a projective coordinate change with A = $ (a_{ij})$ a nonsingular (n+1) $ \times $ (n+1) matrix and if g(x') = f(Ax), where f is a form of degree d in $x_0, x_1, ... x_n$prove that the Hessian matrix transforms as $$ H(g, \textbf{x'}) = A^tH(f, \textbf{x})A$$