2022/12/05 by Qing‐Wen Wang, Wang, Qing-Wen, Long-Sheng Liu +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Algebraic and Geometric Analysis #Digital Image Processing Techniques #FOS: Mathematics #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2212.02146
openalex publication_date 2022/12/05 · openalex created_date 2022/12/18 · openalex updated_date 2026/07/28
Sylvester-type matrix equations have applications in areas including control theory, neural networks, and image processing. In this paper, we establish the necessary and sufficient conditions for the system of Sylvester-type quaternion matrix equations to be consistent and derive an expression of its general solution (when it is solvable). As an application, we investigate the necessary and sufficient conditions for quaternion matrix equations to be consistent and derive a formula for its general solution involving η-Hermicity. As a special case, we also present the necessary and sufficient conditions for the system of two-sided Sylvester-type quaternion matrix equations to have a solution and derive a formula for its general solution (when it is solvable). Finally, we present an algorithm and an example to illustrate the main results of this paper.