Cramer rule for the unique solution of restricted matrix equations over the quaternion skew field

被引：34

作者：

Song, Guang-Jing ^{[1
]}

Wang, Qing-Wen ^{[2
,3
]}

Chang, Hai-Xia ^{[4
]}

机构：

[1] Weifang Univ, Sch Math & Informat Sci, Weifang 261061, Peoples R China

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

[3] Nanyang Technol Univ, Div Math Sci, Singapore 637371, Singapore

[4] Shanghai Finance Univ, Dept Appl Math, Shanghai 201209, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2011年 / 61卷 / 06期

关键词：

Quaternion matrix; Cramer rule; Generalized inverse A(T.S)((2)); GENERALIZED INVERSE A(T; S)((2)); INCONSISTENT LINEAR-EQUATIONS; LEAST-NORM; REPRESENTATION; DETERMINANTS;

D O I：

10.1016/j.camwa.2011.01.026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish the determinantal representations of the generalized inverses A(rT1.S1)((2)), A(lT2.S2)((2)), and A((T1.T2).(S1.S2))((2)) over the quaternion skew field by the theory of the column, and row determinants. In addition, we derive some generalized Cramer rules for the unique solution of some restricted quaternion matrix equations. The findings of this paper extend some known results in the literature. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：1576 / 1589

页数：14

共 31 条

[11] Quaternionic analysis, representation theory and physics [J].

Frenkel, Igor ;

Libine, Matvei .

ADVANCES IN MATHEMATICS, 2008, 218 (06) :1806-1877

[12]

GELFAND I, 1992, FUNKTSIONAL ANAL PRI, V26, P33

[13] DETERMINANTS OF MATRICES OVER NONCOMMUTATIVE RINGS [J].

GELFAND, IM ;

RETAKH, VS .

FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 1991, 25 (02) :91-102

[14] On left eigenvalues of a quaternionic matrix [J].

Huang, LP ;

So, WS .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 323 (1-3) :105-116

[15] Cramer's rule for some quaternion matrix equations [J].

Kyrchei, I. I. .

APPLIED MATHEMATICS AND COMPUTATION, 2010, 217 (05) :2024-2030

[16]

Kyrchei I.I., 2008, J. Math. Sci, V155, P839, DOI DOI 10.1007/S10958-008-9245-6

[17]

KYRCHEI II, ARXIV10050736V1

[18]

LEBIHAN N, 2003, IEEE INT C IM PROC I

[19] Rank equalities related to the generalized inverses AT,S(2), BT1,S1(2) of two matrices A and B [J].

Liu, YH ;

Wei, MS .

APPLIED MATHEMATICS AND COMPUTATION, 2004, 159 (01) :19-28

[20]

Robinson S.M., 1970, Math. Mug., V43, P94, DOI DOI 10.1080/0025570X.1970.11976018

← 1 2 3 4 →