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申論題資訊

試卷:110年 - 110台灣聯合大學系統_碩士班招生考試_電機類:工程數學(B)#104927
科目:研究所、轉學考(插大)◆工程數學
年份:110年
排序:7

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).

申論題內容

(2) Is it true that if Tr(AX) = 0, then AX = 0 61b9a74026f41.jpg (zero matrix)? Prove or disprove your answer.