矩阵方程A+X=AX广义三次矩阵解与绝对值方程的解  

Generalized Cubic Matrix Solutions to Matrix Equation A+X=AX and Solutions to Absolute Value Equation

作　　者：吕洪斌[1] 杨忠鹏 陈梅香 王信存[3] LV Hongbin;YANG Zhongpeng;CHEN Meixiang;WANG Xinchun(School of Mathematics and Statistics,Beihua University,Jilin 132013,Jilin Province,China;School of Mathematics and Finance,Putian University,Putian 351100,Fujian Province,China;Teachers College,Eastern Liaoning University,Dandong 118003,Liaoning Province,China)

机构地区：[1]北华大学数学与统计学院,吉林吉林132013 [2]莆田学院数学与金融学院,福建莆田351100 [3]辽东学院师范学院,辽宁丹东118003

出　　处：《吉林大学学报（理学版）》2020年第3期498-506,共9页Journal of Jilin University:Science Edition

基　　金：吉林省科技发展计划项目(批准号:20190201139JC);福建省自然科学基金(批准号:2018J01426);辽宁省自然科学基金(批准号:20180550758).

摘　　要：应用广义三次矩阵的Jordan标准形,给出AX=A+X有广义三次矩阵解的充要条件及解的形式,并证明由AX=A+X的广义三次矩阵解B所确定的绝对值方程Bx-|x|=b有解.Using Jordan standard form of generalized cubic matrix,we gave the necessary and sufficient conditions that the generalized cubic matrix solutions to the matrix equation AX=A+X existed and the form of the solutions,and proved that the solutions to the absolute value equation Bx-|x|=b the generalized cubic matrix solution B to AX=A+X existed.

关 键 词：广义三次矩阵 JORDAN标准形 矩阵方程 绝对值方程 解 

分 类 号：O151.21[理学—数学]