題組內容

Problem 3. (25 %) Let 62fef3548c340.jpg denote the set of real m✖ n matrices and the set of real n ✖ 1 column vectors, respectively, and let 62fef37f892ea.jpg denote the set of real n ✖ n symmetric positive semidefinite (PSD) matrices. This problem includes two parts as follows: (a) (15 %) Let A62fef3b43d512.jpg with r singular values σ1，... σr, Ur = [u1, ..., ur] consisting of the associated r left singular vectors and Vr= [V1,..., vr] consisting of the associated r right singular vectors.

(ii) find the projection matrix PA such that R(A) =62fef47f24430.jpg；