Solvability of the Sylvester equation AX - XB = C under left semi-tensor product

被引：1
|
作者：
Wang, Naiwen [1 ]
机构：
[1] Shandong Normal Univ, Sch Math & Stat, Jinan 250014, Peoples R China
来源：
MATHEMATICAL MODELLING AND CONTROL | 2022年 / 2卷 / 02期
关键词：
Sylvester matrix equation; left semi-tensor product; solvability; matrix-vector equation; necessary and sufficient condition; MATRIX EQUATIONS;
D O I：
10.3934/mmc.2022010
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper investigates the solvability of the Sylvester matrix equation AX - XB = C with respect to left semi-tensor product. Firstly, we discuss the matrix-vector equation AX - XB = C under semi-tensor product. A necessary and su fficient condition for the solvability of the matrix-vector equation and specific solving methods are studied and given. Based on this, the solvability of the matrix equation AX - XB = C under left semi-tensor product is discussed. Finally, several examples are presented to illustrate the efficiency of the results.
引用
收藏
页码：81 / 89
页数：9
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