Mathematica Pannonica
Volume/Issue:
Volume 29_NS3: Issue 1
Determinant Inequalities for Positive Definite Matrices via Cartwright–Field’s Result for Arithmetic and Geometric Weighted Means
Author:
Silvestru Sever Dragomir Mathematics, 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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Pages:
96–105
Online Publication Date:
06 Mar 2023
Publication Date:
19 May 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≤12∑k=1mPk1−Pkdet2Aj−lIn−1/2−2∑1≤j<k≤mPjPkdetAj+Ak−lIn−1/2≤∑j=1mPjdetAj−1/2−det∑k=1mPkAk−1/2,

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

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Cover Mathematica Pannonica
Mathematica Pannonica
Print ISSN:
0865-2090
Online ISSN:
2786-0752

Editor in Chief: László TÓTH, University of Pécs, Pécs, Hungary

Honorary Editors in Chief:

  • János PINTZ, HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary
  • † Ferenc SCHIPP, Eötvös Loránd University, Budapest, Hungary and University of Pécs, Pécs, Hungary
  • Sándor SZABÓ, University of Pécs, Pécs, Hungary
     

Deputy Editors in Chief:

  • Erhard AICHINGER, JKU Linz, Linz, Austria
  • Ferenc HARTUNG, University of Pannonia, Veszprém, Hungary
  • Ferenc WEISZ, Eötvös Loránd University, Budapest, Hungary

Editorial Board

  • Attila BÉRCZES, University of Debrecen, Debrecen, Hungary
  • István BERKES, Rényi Institute of Mathematics, Budapest, Hungary
  • Károly BEZDEK, University of Calgary, Calgary, Canada
  • György DÓSA, University of Pannonia, Veszprém, Hungary
  • Balázs KIRÁLY – Managing Editor, University of Pécs, Pécs, Hungary
  • Vedran KRCADINAC, University of Zagreb, Zagreb, Croatia 
  • Željka MILIN ŠIPUŠ, University of Zagreb, Zagreb, Croatia
  • Gábor NYUL, University of Debrecen, Debrecen, Hungary
  • Margit PAP, University of Pécs, Pécs, Hungary
  • István PINK, University of Debrecen, Debrecen, Hungary
  • Mihály PITUK, University of Pannonia, Veszprém, Hungary
  • Lukas SPIEGELHOFER, Montanuniversität Leoben, Leoben, Austria
  • Andrea ŠVOB, University of Rijeka, Rijeka, Croatia
  • Csaba SZÁNTÓ, Babeş-Bolyai University, Cluj-Napoca, Romania
  • Jörg THUSWALDNER, Montanuniversität Leoben, Leoben, Austria
  • Zsolt TUZA, University of Pannonia, Veszprém, Hungary

Advisory Board

  • Szilárd RÉVÉSZ – Chair, HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary
  • Gabriella BÖHM
  • György GÁT, University of Debrecen, Debrecen, Hungary

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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)
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