(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.

引用

页数：12

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