OPTIMAL RANKS OF NONLINEAR MATRIX EXPRESSIONS WITH APPLICATIONS

Authors

  • Sihem Guerarra System Dynamics and Control Laboratory, Department of Mathematics and Informatics, University of Oum El Bouaghi
  • Iqbal M. Batiha Department of Mathematics, Faculty of Science and Information Technology, Al Zaytoonah University
  • Nidal Anakira Mathematics Education Program, Faculty of Education and Arts, Sohar University
  • Taki Eddine Oussaeif Department of Mathematics and Computer Science, University of Larbi Ben M'hidi
  • Abed Al-Rahman M. Malkawi Department of Mathematics, Faculty of Arts and Science, Amman Arab University
  • Tala Sasa Department of Mathematics, Faculty of Science, Private Applied Science University

Abstract

This paper presents explicit formulas for the optimal ranks of nonlinear matrixexpressions with respect to four variable matrices. As applications, we derive the optimalranks of the generalized Schur complement and present the optimal ranks of specific non-linear matrix expressions involving four variable matrices, which represent solutions to foursolvable matrix equations. Consequently, we provide equivalent conditions for the existenceof solutions to nonlinear matrix equations.

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Published

2026-08-30

Issue

Volume 31, Number 3, September 2026

Section

Articles