Hello, I have to do a proof and am having trouble starting. The proof is to show how you could use Cholesky decomposition to determine a set of A-orthogonal directions. Cholesky decom. means I can write the symmetric positive definite matrix as A = GG' The textbook gives a way of determining the A-orthogonal set using A. Specifically, v_k = r_k-1 + s_k-1*v_k-1 where v_k is the kth direction vector and r_k-1 is the k-1 residual vector. So we want to choose s_k-1 such that <v_k-1, Av_k> = 0 The textbook then goes onto show: s_k-1 = - <v_k-1, Ar_k-1> / <v_k-1, Av_k-1> So I don't see how using A = GG' helps at all. If anyone could give me a tip on how to start, I'd be thankful.