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