題組內容

Problem 3. 61bad57eb701a.jpgdenote the set of real m x n matrices and the set of real n x 1 column vectors, respectively, and let 61bad594db214.jpg denote the set of real n x n symmetric positive semidefinite (PSD) matrices. This problem includes two parts as follows: 

 (a)  Let A 61bad5c5b7d07.jpg with r singular values σ1,... ,61bad6234e8ab.jpgconsisting of the associated r left singular vectors and 61bad643e62b4.jpg. consisting of the associated r right singular vectors.

(i) Find the range space (i.e., column space) of A, denoted as R(A), and the row space of A (i.e., R(61bad6754836c.jpg)) where 61bad696d46d3.jpg denotes the transpose of A;