The Common Solution of Twelve Matrix Equations over the Quaternions

被引：1

作者：

Yuan, Wei-Jie ^{[1
]}

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

机构：

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

[2] Collaborat Innovat Ctr Marine Artificial Intellig, Shanghai 200444, Peoples R China

来源：

FILOMAT | 2022年 / 36卷 / 03期

基金：

中国国家自然科学基金;

关键词：

General solution; Least-squares solution; Least norm; Quaternion algebra; Real representation; Matrix equation; LEAST-SQUARES SOLUTIONS; GENERAL-SOLUTION; SYSTEM; AX; NORM;

D O I：

10.2298/FIL2203887Y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate a system of twelve quaternion matrix equations. Using the real representation of a quaternion matrix, we first derive the least-squares solution with the least norm to the system. Meanwhile, we establish the solvability conditions and an expression of the general solution to the system when it is consistent.

引用

页码：887 / 903

页数：17

共 50 条

[11] The common solution to six quaternion matrix equations with applications
Wang, Qing-Wen
Chang, Hai-Xia
Ning, Qun
APPLIED MATHEMATICS AND COMPUTATION, 2008, 198 (01) : 209 - 226
[12] The consistency and the general common solution to some quaternion matrix equations
Xu, Xi-Le
Wang, Qing-Wen
ANNALS OF FUNCTIONAL ANALYSIS, 2023, 14 (03)
[13] The consistency and the general common solution to some quaternion matrix equations
Xi-Le Xu
Qing-Wen Wang
Annals of Functional Analysis, 2023, 14
[14] RANKS OF THE COMMON SOLUTION TO SOME QUATERNION MATRIX EQUATIONS WITH APPLICATIONS
Wang, Q. W.
Yu, S. W.
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2012, 38 (01) : 131 - 157
[15] Common least-squares solution to some matrix equations
REHMAN Abdur
WANG Qingwen
上海大学学报(自然科学版), 2017, 23 (02) : 267 - 275
[16] Maximal and Minimal Ranks of the Common Solution of Some Linear Matrix Equations over an Arbitrary Division Ring with Applications
Wang, Qingwen
Song, Guangjing
Liu, Xin
ALGEBRA COLLOQUIUM, 2009, 16 (02) : 293 - 308
[17] INVESTIGATION AND SOLUTION OF MATRIX EQUATIONS OVER ASSOCIATIVE-RINGS
BLYUMIN, SL
MILOVIDOV, SP
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 1994, 34 (02) : 133 - 142
[18] Finite iterative algorithms for a common solution to a group of complex matrix equations
Wu, Ai-Guo
Lv, Lingling
Hou, Ming-Zhe
APPLIED MATHEMATICS AND COMPUTATION, 2011, 218 (04) : 1191 - 1202
[19] ISOMORPHIC SUBRINGS OF MATRIX-RINGS OVER THE INTEGER QUATERNIONS
CHATTERS, AW
COMMUNICATIONS IN ALGEBRA, 1995, 23 (02) : 783 - 802
[20] The reducible solution to a system of matrix equations over the Hamilton quaternion algebra
Liu, Long-Sheng
Wang, Qing-Wen
FILOMAT, 2023, 37 (09) : 2731 - 2742

← 1 2 3 4 5 →