Another determinantal inequality involving partial traces

2020/02/22 by Yongtao Li, Li, Yongtao, Lihua Feng +5
Computer Science · Mathematics · #15A45 #15A60 #47B65 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Matrix Theory and Algorithms #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2002.09652

openalex publication_date 2020/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a positive semidefinite m× m block matrix with each block n-square, then the following determinantal inequality for partial traces holds (tr A)^mn - det(tr₂ A)ⁿ ≥ | det A - det(tr₁ A)^m |, where tr₁ and tr₂ stand for the first and second partial trace, respectively. This result improves a recent result of Lin [14].

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