(R, S)-(Skew) Symmetric Solutions to Matrix Equation AXB = C over Quaternions

被引：1
作者：
Liao, Ruopeng [1 ]
Liu, Xin [2 ]
Long, Sujuan [3 ]
Zhang, Yang [4 ]
机构：
[1] Macau Univ Sci & Technol, Fac Innovat Engn, Sch Comp Sci & Engn, Ave Wai Long, TaiPa 999078, Macau, Peoples R China
[2] Macau Univ Sci & Technol, Macau Inst Syst Engn, Fac Innovat Engn, Ave Wai Long, TaiPa 999078, Macau, Peoples R China
[3] Minjiang Univ, Sch Math & Data Sci, Fuzhou 350108, Fujian, Peoples R China
[4] Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada
来源：
MATHEMATICS | 2024年 / 12卷 / 02期
关键词：
quaternion matrix equation; (R; S)-(skew); symmetric; real representation; REFLEXIVE SOLUTIONS; INVERSE PROBLEMS;
D O I：
10.3390/math12020323
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
(R,S)-(skew) symmetric matrices have numerous applications in civil engineering, information theory, numerical analysis, etc. In this paper, we deal with the (R,S)-(skew) symmetric solutions to the quaternion matrix equation AXB=C. We use a real representation A(tau) to obtain the necessary and sufficient conditions for AXB=C to have (R,S)-(skew) symmetric solutions and derive the solutions when it is consistent. We also derive the least-squares (R,S)-(skew) symmetric solution to the above matrix equation.
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页数：12
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