申論題

Problem 3. (25 %) Let  denote the set of real m✖ n matrices and the set of real n ✖ 1 column vectors, respectively, and let  denote the set of real n ✖ n symmetric positive semidefinite (PSD) matrices. This problem includes two parts as follows:  (b) (10 %) Suppose that A, , 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.