Problem 3. Let
denote the set of real m x n matrices
and the set of real n x 1 column vectors, respectively, and let
denote the set
of real n x n symmetric positive semidefinite (PSD) matrices. This problem
includes two parts as follows:
with r singular values σ1, . ,
consisting of the associated r left singular vectors and
,
consisting of the associated r right singular vectors.
.