In this paper, we establish the solvability conditions and the formula of the general solution to a Sylvester-like quaternion matrix equation. As an application, we give some necessary and sufficient conditions for a system of quaternion matrix equations to be consistent, and present an expression of the general solution of the system when it is solvable. We present an algorithm and an example to illustrate the main results of this paper. The findings of this paper generalize the known results in the literature.
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 η-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.
We derive the solvability conditions and a formula of a general solution to a Sylvester-type matrix equation over Hamilton quaternions. As an application, we investigate the necessary and sufficient conditions for the solvability of the quaternion matrix equation, which involves η-Hermicity. We also provide an algorithm with a numerical example to illustrate the main results of this paper.
We establish the solvability conditions and the formula of the exact general solution of a significant kind of Sylvester-like quaternion matrix equation. As an application, we investigate the η-Herimitan solution of a quaternion matrix equation and give some numerical examples to illustrate the main results of this paper.
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