Mathematica Pannonica
Volume/Issue:
Accepted Manuscript / Online First
Determinant Inequalities for Positive Definite Matrices via Cartwright–Field’s Result for Arithmetic and Geometric Weighted Means
Author:
Silvestru Sever DragomirMathematics, College of Engineering & Science, Victoria University, PO Box 14428, Melbourne City, MC 8001, Australia
DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences, School of Computer Science, & Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa

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Online Publication Date:
06 Mar 2023
Publication Date:
06 Mar 2023
Article Category:
Research Article
DOI:
https://doi.org/10.1556/314.2023.00008
Keywords:
Positive definite matrices; determinants; inequalities
Open access

Assume that Aj , j ∈ {1, … , m} are positive definite matrices of order n. In this paper we prove among others that, if 0 < l In ≤ Aj , j ∈ {1, … , m} in the operator order, for some positive constant l, and In is the unity matrix of order n, then

o ≤ 1 2 ∑ k = 1 m P k 1 − P k det 2 A j − l I n − 1 / 2 − 2 ∑ 1 ≤ j < k ≤ m P j P k det A j + A k − l I n − 1 / 2 ≤ ∑ j = 1 m P j det A j − 1 / 2 − det ∑ k = 1 m P k A k − 1 / 2 ,

where Pk ≥ 0 for k ϵ {1, …, m} and ∑ j = 1 m P j = 1 .

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Mathematica Pannonica
Print ISSN:
0865-2090
Online ISSN:
2786-0752
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Editor in Chief: László TÓTH (University of Pécs)

Honorary Editors in Chief:

  • † István GYŐRI (University of Pannonia, Veszprém)
  • János PINTZ (Rényi Institute of Mathematics)
  • Ferenc SCHIPP (Eötvös University Budapest and University of Pécs)
  • Sándor SZABÓ (University of Pécs)
     

Deputy Editors in Chief:

  • Erhard AICHINGER (JKU Linz)
  • Ferenc HARTUNG (University of Pannonia, Veszprém)
  • Ferenc WEISZ (Eötvös University, Budapest)

Editorial Board

  • György DÓSA (University of Pannonia, Veszprém)
  • István BERKES (Rényi Institute of Mathematics)
  • Károly BEZDEK (University of Calgary)
  • Balázs KIRÁLY – Managing Editor (University of Pécs)
  • Vedran KRCADINAC (University of Zagreb) 
  • Željka MILIN ŠIPUŠ (University of Zagreb)
  • Margit PAP (University of Pécs)
  • Mihály PITUK (University of Pannonia, Veszprém)
  • Jörg THUSWALDNER (Montanuniversität Leoben)
  • Zsolt TUZA (University of Pannonia, Veszprém)

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  • György GÁT (University of Debrecen)

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Mathematica Pannonica
Language English
Size A4
Year of
Foundation		 1990
Volumes
per Year		 1
Issues
per Year		 2
Founder Akadémiai Kiadó
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ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)

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