申論題

Problem 3. (25 %) Let denote the set of real m✖ n matrices and the set of real n ✖ 1 column vectors, respectively, and let denote the set of real n ✖ n symmetric positive semidefinite (PSD) matrices. This problem includes two parts as follows: (a) (15 %) Let A with r singular values σ₁，... σ_r, Ur = [u₁, ..., u_r] consisting of the associated r left singular vectors and V_r= [V₁,..., v_r] consisting of the associated r right singular vectors.