论文标题
使用应用
The general solutions to some systems of Sylvester-type quaternion matrix equations with an application
论文作者
论文摘要
Sylvester型矩阵方程在控制理论，神经网络和图像处理等领域具有应用。在本文中，我们建立了Sylvester型季节矩阵方程系统的必要条件，以保持一致，并得出其一般解决方案的表达（当它是可解决的时）。作为应用程序，我们调查了四元矩阵方程的必要条件，以保持一致，并为其涉及$η$热的一般解决方案提供公式。作为一种特殊情况，我们还为双面Sylvester型Quaternion矩阵方程的系统提供了必要和充分的条件，以具有解决方案并为其通用解决方案提供一个公式（当它可溶解时）。最后，我们提出了一种算法和一个示例，以说明本文的主要结果。
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.
