An Oppenheim type inequality for positive definite block matrices

Abstract

We present an Oppenheim type determinantal inequality for positive definite block matrices. Recently, Lin [Linear Algebra Appl. 452 (2014) 1--6] proved a remarkable extension of Oppenheim type inequality for block matrices, which solved a conjecture of Günther and Klotz. There is a requirement that two matrices commute in Lin's result. The motivation of this paper is to obtain another natural and general extension of Oppenheim type inequality for block matrices to get rid of the requirement that two matrices commute.

12 pages. Any comments and suggestions are welcome. E-mail addresses: [email protected] (Yongtao Li), [email protected] (Yuejian Peng, corresponding author). Linear and Multilinear Algebra (2021). Linear and Multilinear Algebra, 2021