Let A E Rnx" be a symmetric matrix in Rnx. Let A1, ..., An be n distinct eigenvalues of A satisfying 1 > 12 > . . . > An > 0 and u1, u2, . .., Un be the corresponding eigenvectors. Let's consider the following minimization problem: minimize f(x) := ||A - xx7117 xERn (a) Compute Vf(x) and V2 f(x). (b) Find all the stationary points of f(x). (c) Among all the stationary points, which has the largest function value (i.e., which is the global maximizer)? (d) Among all the stationary points, which has the smallest function value (i.e., which is the global minimizer)? (e) Show that all the remaining stationary points (i.e., that are neither global minimizer nor maximizer) have the Hessian matrix V2f(x) that is neither PSD nor NSD. (Hint: A matrix A is NSD (negative semi-definite) iff and only if - A is PSD)