Properties and Applications of Generalized Numerical Radius in Block Matrix Structures

Authors

  • Rajaa Al-Naimi University of Petra https://orcid.org/0000-0003-4233-3500
  • Manal Al-Labadi University of Petra
  • Wasim Audeh University of Petra
  • Jamal Oudetallah University of Petra
  • Mutti-Ur Rehman Center of Research and Innovation, Asia International University
  • Dheyaa Alangood University of Tikrit

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i4.6813

Keywords:

Numerical radius, matrix inequality

Abstract

In this paper, we prove several results that generalize fundamental properties of numerical radius and generalized numerical radius. Among our proven inequalities, we establish theorems for matrices A ∈ Mm(Mn), where Mm(Mn) represents the set of all m × m block complex matrices with each block belonging to Mn(C). Furthermore, we demonstrate that if A ∈ M2(Mn) is a positive semidefinite matrix, then w(2)(A) is positive semidefinite, and if A ∈ Mm(M2) is a positive semidefinite matrix, then
w(1)(A) is positive semidefinite. Here, w(1)(A) denotes the first partial matrix of numerical radius and w(2)(A) denotes the second partial matrix of numerical radius, respectively. Additionally, we develop relationships with classical matrix parameters and establish structural theorems for block matrices.

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Published

2025-11-05

Issue

Vol. 18 No. 4: (October 2025)

Section

Functional Analysis

License

Copyright (c) 2025 Rajaa Al-Naimi, Manal Al-Labadi, Wasim Audeh, Jamal Oudetallah, Mutti-Ur Rehman, Dheyaa Alangood

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How to Cite

Properties and Applications of Generalized Numerical Radius in Block Matrix Structures. (2025). European Journal of Pure and Applied Mathematics, 18(4), 6813. https://doi.org/10.29020/nybg.ejpam.v18i4.6813