An equivalence canonical form of a matrix triplet over an arbitrary division ring with applications

作     者：WANG QingWen van der WOUDE J. W. YU ShaoWen 

作者机构：Department of Mathematics Shanghai University Shanghai 200444 China Faculty of Electrical Engineering Mathematics and Computer ScienceDelft University of Technology Mekelweg 4 2628 CD Delft The Netherlands Department of Mathematics East China University of Science and Technology Shanghai 200237 China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2011年第54卷第5期

页      面：907-924页

核心收录：

学科分类：1305[艺术学-设计学（可授艺术学、工学学位）] 13[艺术学] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China (GrantNo. 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 Shanghai Leading Academic Discipline Project (Grant No. J50101) 

主　　题：矩阵方程 应用程序 规范形式 等价 除环 三重分解 彩色图像 表达式 

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.