1. The problem statement, all variables and given/known data Consider the function f(a)= 1 ∫ [g(x)-(anxn+an-1xn-1+...+a0)]2 dx 0 where a=(a0,a1,...an) and g is some known function defined on [0,1]. From this, we can show that Thus, the Hessian of f at a = [2/(j+k+1)] j=0,1,2,...n; k=0,1,2,...,n. Fact: This Hessian matrix is positive definite. Now how can we prove that this (n+1) x (n+1) matrix is positive definite? (i.e. vT (Hessian) v >0 for all v E Rn+1, v≠0.) When I multiply out the vT (Hessian) v, it just doesn't seem clear to me at all that it is >0. 2. Relevant equations N/A 3. The attempt at a solution Shown above. Any help is appreciated!