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arXiv · 2002.12560

Extensions of Brunn-Minkovski's inequality to multiple matrices

Yongtao Li·Lihua Feng
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Abstract

Yuan and Leng (2007) gave a generalization of Ky Fan's determinantal inequality, which is a celebrated refinement of the fundamental Brunn-Minkowski inequality $(\det (A+B))^{1/n} \ge (\det A)^{1/n} +(\det B)^{1/n}$, where $A$ and $B$ are positive semidefinite matrices. In this note, we first give an extension of Yuan-Leng's result to multiple positive definite matrices, and then we further extend the result to a larger class of matrices whose numerical ranges are contained in a sector. Our result improves a recent result of Liu [Linear Algebra Appl. 508 (2016) 206--213].

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Yongtao Li, Lihua Feng. 2020-02-28. Extensions of Brunn-Minkovski's inequality to multiple matrices. https://doi.org/10.1016/j.laa.2020.05.037

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