A determinantal inequality for positive semidefinite matrices

Abstract

Let A, B, C be n à 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 â (det(A + C) + det(B + C)) ⥠det(A + B) â (det A + det B).