Solvability and uniqueness criteria for generalized Sylvester-type equations

被引：13

作者：

De Teran, Fernando ^{[1
]}

Iannazzo, Bruno ^{[2
]}

Poloni, Federico ^{[3
]}

Robol, Leonardo ^{[4
]}

机构：

[1] Univ Carlos III Madrid, Dept Matemat, Avda Univ 30, Leganes 28911, Spain

[2] Univ Perugia, Dipartimento Matemat & Informat, Via Vanvitelli 1, I-06123 Perugia, Italy

[3] Univ Pisa, Dipartimento Informat, Largo B Pontecorvo 3, I-56127 Pisa, Italy

[4] CNR, ISTI, Area Ric, Via G Moruzzi 1, I-56124 Pisa, Italy

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2018年 / 542卷

关键词：

Sylvester equation; Eigenvalues; Matrix pencil; Matrix equation; LINEAR MATRIX EQUATIONS;

D O I：

10.1016/j.laa.2017.07.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide necessary and sufficient conditions for the generalized star-Sylvester matrix equation, AXB+(CXD)-D-star = E, to have exactly one solution for any right-hand side E. These conditions are given for arbitrary coefficient matrices A, B, C, D (either square or rectangular) and generalize existing results for the same equation with square coefficients. We also review the known results regarding the existence and uniqueness of solution for generalized Sylvester and star-Sylvester equations. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：501 / 521

页数：21

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