申論題

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 S" denote the set of real n x n symmetric positive semidefinite (PSD) matrices. This problem includes two parts as follows: 

(b) Suppose that A, X , and Tr(A) denotes the trace of A (i.e., the sum of all the diagonal elements of A).

(ii) Is it true that if Tr(AX) = 0, then AX = 0 (zero matrix)? Prove or disprove your answer.