題組內容

Problem 3.  Let 61b9a6d184571.jpg denote the set of real m x n matrices and the set of real n x 1 column vectors, respectively, and let 61b9a6e6ad6c1.jpg denote the set of real n x n symmetric positive semidefinite (PSD) matrices. This problem includes two parts as follows:

 (ii)  Suppose that A, X61b9a7060422c.jpg, and Tr(A) denotes the trace of A (i.e., the sum of all the diagonal elements of A).

(1) Is Tr(AX) ≥ 0 true?