Solving a System of Sylvester-like Quaternion Matrix Equations

oleh: Ruo-Nan Wang, Qing-Wen Wang, Long-Sheng Liu

Format: Article
Diterbitkan: MDPI AG 2022-05-01

Deskripsi

Using the ranks and Moore-Penrose inverses of involved matrices, in this paper we establish some necessary and sufficient solvability conditions for a system of Sylvester-type quaternion matrix equations, and give an expression of the general solution to the system when it is solvable. As an application of the system, we consider a special symmetry solution, named the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-Hermitian solution, for a system of quaternion matrix equations. Moreover, we present an algorithm and a numerical example to verify the main results of this paper.