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

被引：29
作者：
Kyrchei, Ivan [1 ]
机构：
[1] NAS Ukraine, Pidstrygach Inst Appl Problems Mech & Math, Str Naukova 3b, UA-79060 Lvov, Ukraine
来源：
ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2018年 / 28卷 / 05期
关键词：
Matrix equation; Sylvester matrix equation; Lyapunov matrix equation; Cramer Rule; Quaternion matrix; Noncommutative determinant; WEIGHTED DRAZIN INVERSE; LEAST-SQUARES SOLUTIONS; DETERMINANTAL REPRESENTATIONS; SKEW FIELD; SIMULTANEOUS DECOMPOSITION; SYSTEM; NORM; AX; SOLVABILITY; FORMULAS;
D O I：
10.1007/s00006-018-0909-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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<tex-math 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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页数：26
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