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 G\"{u}nther 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.
Keywords
Cite
@article{arxiv.2109.02819,
title = {An Oppenheim type inequality for positive definite block matrices},
author = {Yongtao Li and Yuejian Peng},
journal= {arXiv preprint arXiv:2109.02819},
year = {2024}
}
Comments
12 pages. Any comments and suggestions are welcome. E-mail addresses: ytli0921@hnu.edu.cn (Yongtao Li), ypeng1@hnu.edu.cn (Yuejian Peng, corresponding author). Linear and Multilinear Algebra (2021). Linear and Multilinear Algebra, 2021