Popoviciu type inequalities for determinants. Issue 20 (19th December 2022)

• Record Type: Journal Article
• Authors: Mao, Yanling; Mao, Yaping
• Is Part Of: Linear & multilinear algebra. Volume 70:Issue 20(2022)
• Page Start: 5032
• Page End: 5039
• Publication Date: 2022-12-19
• Subjects: Popoviciu's inequality -- determinant inequality -- positive definite matrix -- sectorial matrix; 15A60 -- 15A45; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2021.1902464
• Languages: English
• ISSNs: 0308-1087

Abstract

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.