The question is:

Suppose that lim , where is a local minimizer of the nonlinear function . Assume that is symmetric positive definite. Prove that the sequence converges linearly if and only if converges linearly. Prove that the two sequences converge at the same rate, regardless of what the rate is. What is the relationship between the rate constant for the two sequences?

(I guess we may use the orthogonal diagonalization of a symmetric matrix and and ...... But I got stuck here. So what's your answer?)