Year: 2025
Type: article
Abstract: This paper primarily investigates the solutions to the system of equations A1XB1=C1 and A2XB2=C2. This system generalizes the classical equation AXB=C, as well as the system of equations AX=B and XC=D, and finds broad applications in control theory, signal processing, networking, optimization, and other related fields. Various methods for solving this system are introduced, including the generalized inverse method, the vec-operator method, matrix decomposition techniques, Cramer’s rule, and iterative algorithms. Based on these approaches, the paper discusses general solutions, symmetric solutions, Hermitian solutions, and other special types of solutions over different algebraic structures, such as number fields, the real field, the complex field, the quaternion division ring, principal ideal domains, regular rings, strongly *-reducible rings, and operators on Banach spaces. In addition, matrix systems related to the system A1XB1=C1 and A2XB2=C2 are also explored.
Source: Symmetry
DOI: 10.3390/sym17081307
Authors: Qing-Wen Wang, Zi-Han Gao, Yu-Fei Li
Institution: Shanghai 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: $2,896
Award: G7068616604
OpenAlex ID: W4413128188