Investigation of some Sylvester-type quaternion matrix equations with multiple unknowns

被引：6

作者：

Zhang, Chong-Quan ^{[1
,2
]}

Wang, Qing-Wen ^{[1
,2
]}

Dmytryshyn, Andrii ^{[3
]}

He, Zhuo-Heng ^{[1
,2
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

[2] Shanghai Univ, Newtouch Ctr Math, Shanghai 200444, Peoples R China

[3] Orebro Univ, Sch Sci & Technol, Orebro, Sweden

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2024年 / 43卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Linear matrix equation; Inner inverse; General solution; Quaternion; Solvability; NONNEGATIVE-DEFINITE; AX; SYSTEMS; AXB+CYD;

D O I：

10.1007/s40314-024-02706-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the solvability conditions of some Sylvester-type quaternion matrix equations. We establish some practical necessary and sufficient conditions for the existence of solutions of a Sylvester-type quaternion matrix equation with five unknowns through the corresponding equivalence relations of the block matrices. Moreover, we present some solvability conditions to some Sylvester-type quaternion matrix equations, including those involving Hermicity. The findings of this article extend related known results.

引用

页数：26

共 43 条

[31] OZGULER AB, 1991, SIAM J MATRIX ANAL A, V12, P581
[32] THE EQUATIONS AX-YB=C AND AX-XB=C IN MATRICES
ROTH, WE
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1952, 3 (03) : 392 - 396
[33] Computational Methods for Linear Matrix Equations
Simoncini, V.
[J]. SIAM REVIEW, 2016, 58 (03) : 377 - 441
[34] An iterative solution to coupled quaternion matrix equations
Song, Caiqin
Chen, Guoliang
Zhang, Xiangyun
[J]. FILOMAT, 2012, 26 (04) : 809 - 826
[35] New results on condensed Cramer's rule for the general solution to some restricted quaternion matrix equations
Song, Guang-Jing
Dong, Chang-Zhou
[J]. JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2017, 53 (1-2) : 321 - 341
[36] ALMOST NONINTERACTING CONTROL BY MEASUREMENT FEEDBACK
VANDERWOUDE, JW
[J]. SYSTEMS & CONTROL LETTERS, 1987, 9 (01) : 7 - 16
[37] Some matrix equations with applications
Wang, Qing-Wen
He, Zhuo-Heng
[J]. LINEAR & MULTILINEAR ALGEBRA, 2012, 60 (11-12) : 1327 - 1353
[38] A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity
Wang, QW
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 384 : 43 - 54
[39] On solutions of matrix equation AXB+CYD = F
Xu, GP
Wei, MS
Zheng, DS
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1998, 279 (1-3) : 93 - 109
[40] Common hermitian and positive solutions to the adjointable operator equations AX = C, XB = D
Xu, Qingxiang
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 429 (01) : 1 - 11

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