四元数体上李雅普诺夫矩阵方程解的特征确定法

Characteristic Determinative Method of Lyapunov Matrix Equation Solution on Quaternion Field

利用四元数的矩阵形式定义四元数的一种特征值,通过求解四元数李雅普诺夫方程,给出四元数体上一般形式的李雅普诺夫矩阵方程的分类方法及解的特征确定法,并给出方程有解的充要条件及解的表达式.

A characteristic value of the quaternion numbers has been defined by using its matrix form. The classification method of generic Lyapunov matrix equation, the characteristic determinative method of solution, a necessary and sufficient condition of the equation having solution and an expression of solution are presented by finding solutions of Lyapunov matrix equation of the quaternion numbers.