Determinantal inequality, Positive definite matrix


Let A, B, C be n × n positive semidefinite matrices. It is known that det(A + B + C) + det C ≥ det(A + C) + det(B + C), which includes det(A + B) ≥ det A + det B as a special case. In this article, a relation between these two inequalities is proved, namely, det(A + B + C) + det C − (det(A + C) + det(B + C)) ≥ det(A + B) − (det A + det B).



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