Work

An $ \eta $-Hermitian solution to a two-sided matrix equation and a system of matrix equations over the skew-field of quaternions

Year: 2025

Type: article

Abstract: This study investigated $ {\eta} $-Hermitian solutions to a two-sided matrix equation and a system of matrix equations over the skew-field of quaternions. We employed solvability conditions to identify the general solution for this system. This method deduces the Moore-Penrose inverse, and the rank equalities for the system's coefficients. We utilized these strategies to develop an algorithm that can compute general solutions. We also used these algorithms in numerical instances to verify the theoretical results.

Source: AIMS Mathematics

DOI: 10.3934/math.2025352

Authors: Mahmoud S. Mehany, Faizah D. Alanazi

Institutions: Ain Shams University, Universidade Nova de Lisboa, Northern Border University

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funders: Ain Shams University, Northern Border University