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Determinant Inequalities for Positive Definite Matrices Via Diananda’s Result for Arithmetic and Geometric Weighted Means

Determinant Inequalities for Positive Definite Matrices Via Diananda’s Result for Arithmetic and... AbstractIn this paper we prove among others that, if (Aj)j=1,...,m are positive definite matrices of order n ≥ 2 and qj ≥ 0, j = 1, ..., m with ∑j=1mqj=1$$\sum\nolimits_{j = 1}^m {{q_j} = 1} $$, then0≤11−mini∈{1,…,m}{ qi }×[ ∑​i=1mqi(1−qi)[ det(Ai) ]−1−2n+1∑​1≤i<j≤mqiqj[ det(Ai+Aj) ]−1 ]≤∑​i=1mqi[ det(Ai) ]−1−[ det(∑​i=1mqiAi) ]−1≤1mini∈{1,…,m}{ qi }×[ ∑​i=1mqi(1−qi)[ det(Ai) ]−1−2n+1∑​1≤i<j≤mqiqj[ det(Ai+Aj) ]−1 ]. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of West University of Timisoara - Mathematics de Gruyter

Determinant Inequalities for Positive Definite Matrices Via Diananda’s Result for Arithmetic and Geometric Weighted Means

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References (11)

Publisher
de Gruyter
Copyright
© 2023 Silvestru Sever Dragomir, published by Sciendo
ISSN
1841-3307
eISSN
1841-3307
DOI
10.2478/awutm-2023-0003
Publisher site
See Article on Publisher Site

Abstract

AbstractIn this paper we prove among others that, if (Aj)j=1,...,m are positive definite matrices of order n ≥ 2 and qj ≥ 0, j = 1, ..., m with ∑j=1mqj=1$$\sum\nolimits_{j = 1}^m {{q_j} = 1} $$, then0≤11−mini∈{1,…,m}{ qi }×[ ∑​i=1mqi(1−qi)[ det(Ai) ]−1−2n+1∑​1≤i<j≤mqiqj[ det(Ai+Aj) ]−1 ]≤∑​i=1mqi[ det(Ai) ]−1−[ det(∑​i=1mqiAi) ]−1≤1mini∈{1,…,m}{ qi }×[ ∑​i=1mqi(1−qi)[ det(Ai) ]−1−2n+1∑​1≤i<j≤mqiqj[ det(Ai+Aj) ]−1 ].

Journal

Annals of West University of Timisoara - Mathematicsde Gruyter

Published: Jun 1, 2023

Keywords: Positive definite matrices; Determinants; Inequalities; 47A63; 26D15; 46C05

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