3. Let A be an n x n positive semidefinite matrix. Let B be an nx n positive definite matrix. Then we have Klein's inequality tr(A(ln(A) – In(B))) > tr(A – B). (i) Let 1/2 -1/2) -i/2 1/2 (1/2 B = (O 1/2). A = Calculate the left-hand side and the right-hand side of the inequality. (ii) When is the inequality an equality?

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