文献类型：期刊文献

中文题名：An equivalence canonical form of a matrix triplet over an arbitrary division ring with applications

英文题名：An equivalence canonical form of a matrix triplet over an arbitrary division ring with applications

作者：Wang QingWen[1];van der Woude, J. W.[2];Yu ShaoWen[3]

机构：[1]Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China;[2]Delft Univ Technol, Fac Elect Engn Math & Comp Sci, NL-2628 CD Delft, Netherlands;[3]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2011

卷号：54

期号：5

起止页码：907

中文期刊名：Science China Mathematics

外文期刊名：SCIENCE CHINA-MATHEMATICS

收录：;Scopus;WOS:【SCI-EXPANDED(收录号:WOS:000290768800004)】；PubMed;

基金：This research was supported by National Natural Science Foundation of China (Grant No. 60672160), the Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20093108110001), the Scientific Research Innovation Foundation of Shanghai Municipal Education Commission (Grant No. 09YZ13), the Netherlands Organization for Scientific Research (NWO), Singapore MoE Tier 1 Research Grant RG60/07, and Shanghai Leading Academic Discipline Project (Grant No. J50101). The authors cordially thank the referees for their careful reading and helpful comments.

语种：英文

中文关键词：division ring; linear matrix equation; equivalence canonical form of a matrix triplet; decomposition

外文关键词：division ring; linear matrix equation; equivalence canonical form of a matrix triplet; decomposition

摘要：We in this paper give a decomposition concerning the general matrix triplet over an arbitrary divisionring F with the same row or column numbers. We also design a practical algorithm for the decomposition of thematrix triplet. As applications, we present necessary and suficient conditions for the existence of the generalsolutions to the system of matrix equations DXA = C1, EXB = C2, F XC = C3 and the matrix equation AXD + BY E + CZF = Gover F. We give the expressions of the general solutions to the system and the matrix equation when thesolvability conditions are satisfied. Moreover, we present numerical examples to illustrate the results of thispaper. We also mention the other applications of the equivalence canonical form, for instance, for the compressionof color images.
We in this paper give a decomposition concerning the general matrix triplet over an arbitrary division ring F with the same row or column numbers. We also design a practical algorithm for the decomposition of the matrix triplet. As applications, we present necessary and sufficient conditions for the existence of the general solutions to the system of matrix equations DXA = C-1, EXB = C-2, FXC = C-3 and the matrix equation AXD + BYE + CZF = G over F. We give the expressions of the general solutions to the system and the matrix equation when the solvability conditions are satisfied. Moreover, we present numerical examples to illustrate the results of this paper. We also mention the other applications of the equivalence canonical form, for instance, for the compression of color images.