一个四元数矩阵方程组的η-Hermitian解

doi:10.3969/j.issn.1007-2861.2013.06.010

上海大学学报(自然科学版) ›› 2013, Vol. 19 ›› Issue (6): 606-610.doi: 10.3969/j.issn.1007-2861.2013.06.010

一个四元数矩阵方程组的η-Hermitian解

陈笛1,吴维峰2

1. 上海大学理学院, 上海 200444; 2. 潍坊工程职业学院会计与统计学院, 山东潍坊 262500

出版日期:2013-12-30 发布日期:2013-12-30
通讯作者: 吴维峰(1963—), 男, 副教授, 研究方向为矩阵论及其应用. E-mail:wwfweifang@126.com
作者简介:吴维峰(1963—), 男, 副教授, 研究方向为矩阵论及其应用.
基金资助:
国家自然科学基金资助项目(11171205); 上海市教委创新基金资助项目(13ZZ080)

η-Hermitian Solutions to a System of Quaternion Matrix Equations

CHEN Di1,WU Wei-feng2

1. College of Sciences, Shanghai University, Shanghai 200444, China;2. Accounting and Statistics School of Mathematics,Weifang Engineering Vocational College, Weifang 262500, Shandong, China

Online:2013-12-30 Published:2013-12-30

摘要/Abstract

摘要： 对于四元数矩阵方程组AXA^η∗+ BYB^η∗= E, CYC^η∗+ DZD^η∗= F , 首先运用 4 个矩阵的奇异值分解, 给出四元数矩阵方程组有η-Hermitian解的充要条件; 然后, 利用该充要条件给出矩阵方程组η-Hermitian解的表达式.

关键词: 矩阵分解, 四元数矩阵, 秩

Abstract: This paper derives a necessary and sufficient condition for the existence of the η-Hermitian solutions to the quaternion matrix equationsAXA^η∗+ BYB^η∗= E, CYC^η∗+ DZD^η∗= F by using the singular value decomposition of four matrices, and gives an expression of the η-Hermitian solutions to the quaternion matrix equations.

Key words: matrix decomposition, quaternion matrix, rank

中图分类号:

O 151.21

陈笛1,吴维峰2. 一个四元数矩阵方程组的η-Hermitian解[J]. 上海大学学报(自然科学版), 2013, 19(6): 606-610.

CHEN Di1,WU Wei-feng2. η-Hermitian Solutions to a System of Quaternion Matrix Equations[J]. Journal of Shanghai University（Natural Science Edition）, 2013, 19(6): 606-610.

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一个四元数矩阵方程组的η-Hermitian解

η-Hermitian Solutions to a System of Quaternion Matrix Equations

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