Cramer’s Rules for Sylvester Quaternion Matrix Equation and Its Special Cases

被引：0
作者：
Ivan Kyrchei
机构：
[1] Pidstrygach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine,
来源：
Advances in Applied Clifford Algebras | 2018年 / 28卷
关键词：
Matrix equation; Sylvester matrix equation; Lyapunov matrix equation; Cramer Rule; Quaternion matrix; Noncommutative determinant; Primary 15A24; Secondary 15A09; 15A15; 15B33;
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摘要：
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 equation A1X1B1+A2X2B2=C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbf{A}_{1}{} \mathbf{X}_{1}{} \mathbf{B}_{1}+ \mathbf{A}_{2}{} \mathbf{X}_{2}{} \mathbf{B}_{2}=\mathbf{C}$$\end{document} and 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.
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