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:
, and Tr(A) denotes the trace of A (i.e.,
the sum of all the diagonal elements of A).
(zero matrix)? Prove or disprove your answer.