Ranks of solutions of the linear matrix equation AX plus YB = C

doi:10.1016/j.camwa.2006.05.011

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	Ranks of solutions of the linear matrix equation AX plus YB = C
	Yong Hui Liu
	2006-09-01
发表期刊	COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN	0898-1221
卷号	52 期号:6-7 页码:861-872
摘要	For a consistent complex matrix equation AX + YB = C, we solve the following two problems: (1) the maximal and minimal ranks of a pair of solutions X and Y to AX + YB = C, and (2) the maximal and minimal ranks of four real matrices X-0, X-1, Y-0, and Y-1 in a pair of solutions X = X-0 + iX(1) and Y = Y-0 + iY(1) to AX + YB = C. We also give a necessary and sufficient condition for matrix equations A(i)X(i) + YiBi = C (i = 1, 2) to have common solutions. (c) 2006 Elsevier Ltd. All rights reserved.
关键词	matrix equation solvability condition general solution maximal rank minimal rank common solution generalized inverse matrix rank method
DOI	10.1016/j.camwa.2006.05.011
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000243017700005
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/3789
专题	中国科学院数学与系统科学研究院
通讯作者	Yong Hui Liu
作者单位	1.Shanghai Finance Univ, Dept Appl Math, Shanghai 201209, Peoples R China 2.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Yong Hui Liu. Ranks of solutions of the linear matrix equation AX plus YB = C[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2006,52(6-7):861-872.
APA	Yong Hui Liu.(2006).Ranks of solutions of the linear matrix equation AX plus YB = C.COMPUTERS & MATHEMATICS WITH APPLICATIONS,52(6-7),861-872.
MLA	Yong Hui Liu."Ranks of solutions of the linear matrix equation AX plus YB = C".COMPUTERS & MATHEMATICS WITH APPLICATIONS 52.6-7(2006):861-872.