Cramer’s Rules for Sylvester Quaternion Matrix Equation and Its Special Cases
Cramer’s Rules for Sylvester Quaternion Matrix Equation and Its Special Cases
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DOI：
10.1007/s00006-018-0909-0
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发表时间：
2018-09
影响因子：
1.5
通讯作者：
Ivan Kyrchei
中科院分区：
文献类型：
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作者：
Ivan Kyrchei
在四元数列行行列式理论的框架下，利用作者以前得到的Moore-Penrose逆的行列式表示，我们得到了四元数双边广义Sylvester矩阵方程的解(类似于Cramer规则)的显式行列式表示式，以及当它的第一项或两项都是单侧时的所有特例。最后，给出了Like-Lyapunov方程解的行列式表示。
Within the framework of the theory of quaternion column-row determinants and using determinantal representations of the Moore–Penrose inverse previously obtained by the author, we get explicit determinantal representation formulas of solutions (analogs of Cramer’s Rule) to the quaternion two-sided generalized Sylvester matrix equationand its all special cases when its first term or both terms are one-sided. Finally, determinantal representations of solutions to like-Lyapunov equations are derived.