Open AccessA simple method for solving matrix equations $ AXB = D $ and $ GXH = C $
Author(s) -
Huiting Zhang,
Hairui Zhang,
Lina Liu,
Yongxin Yuan
Publication year - 2020
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021156
Subject(s) - simple (philosophy) , hermitian matrix , mathematics , matrix (chemical analysis) , matrix difference equation , mathematical analysis , pure mathematics , differential equation , chemistry , riccati equation , philosophy , epistemology , chromatography
A simple method to solve the common solution to the pair of linear matrix equations $ AXB = D $ and $ GXH = C $ is introduced. Some necessary and sufficient conditions for the existence of a common solution, and two expressions for the general common solution of the equation pair are provided by the proposed method. Subsequently, the results are applied to determine the solution of the matrix equation $ AXB+GYH = D $ and the Hermitian solution of the matrix equation $ AXB = D. $