I've been trying to solve this problem for a long time, but I don't know exactly how to start:
Translation: M is square dxd, we want to show that f belongs to C^2 in R^d. After we want to calculate the Hessian matrix and the gradient of the function f(x)
What I've been thinking is to expand M=mij and calculate by hand but I think that would take a long time.(that works well to show it belongs to C^2(R^d)). Another way I thought it was to use somehow the expansion: f(a+h)=f(a)++1/2+||h||^2*e(h) where <,>=||.||
Thank you all (sorry for bad format of equations, I'm a beginner)