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

页码：81 / 89

页数：9

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