Popoviciu type inequalities for determinants. Issue 20 (19th December 2022) - Mao, Yanling; Mao, Yaping
Abstract : The Popoviciu inequality is known as a weighted version of the celebrated Aczel inequality. In this paper, we establish an analogue of the Popoviciu inequality for the determinants of positive definite matrices, and then we extend our result to the case where the underlying matrices are sectorial matrices, i.e. matrices whose field of values (or numerical range) are contained in a sector.