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Ranks of the Common Solution to Six Quaternion Matrix Equations

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文摘 A new expression is established for the common solution to six classical linear quaternion matrix equations A_1X = C_1,XB_1 = C_3,A_2X = C_2,XB_2 = C_4,A_3XB_3 = C_5,A4XB_4 = C_6 which was investigated recently by Wang,Chang and Ning (Q.Wang,H.Chang,Q.Ning,The common solution to six quaternion matrix equations with applications,Appl.Math.Comput.195:721-732 (2008)).Formulas are derived for the maximal and minimal ranks of the common solution to this system.Moreover,corresponding results on some special cases are presented.As an application,a necessary and sufficient condition is presented for the invariance of the rank of the general solution to this system.Some known results can be regarded as the special cases of the results in this paper.
来源 Acta Mathematicae Applicatae Sinica-English Series ,2011,27(3):443-462 【核心库】
DOI 10.1007/s10255-011-0083-9
关键词 system of matrix equations ; quaternion matrix ; minimal rank ; maximal rank ; linear matrix expression ; generalized inverse
地址

Department of Mathematics,Shanghai University, Shanghai, 200444

语种 英文
文献类型 研究性论文
ISSN 0168-9673
学科 数学
基金 National Natural Science Foundation of Shanghai ;  国家教育部高等学校博士学科点专项科研基金 ;  上海市重点学科建设项目
文献收藏号 CSCD:4218002

参考文献 共 27 共2页

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