摘要
主要利用广义逆矩阵和乘法正则补元来研究一类矩阵方程的可解性.首先,在交换半环上讨论矩阵方程AXB=C的可解性;其次,在加法可消交换半环上讨论矩阵方程组{A_(1)XB_(1)=C_(1),A_(2)XB_(2)=C_(2)的可解性及其有解时一般解的表达式;最后,得出矩阵方程AXB+CYD=E可解的充要条件.
This paper deals with the solvability of a class of matrix equations mainly by using generalized inverse matrices and multiplicative regular complements.First,we discuss the solvability of matrix equation AXB=C over commutative semirings,and then,consider the solvability of the system of matrix equations A_(1)XB_(1)=C_(1),A_(2)XB_(2)=C_(2).Moreover,we give the expression of its general solutions on additive cancellable commutative semirings.Finally,we give some necessary and sufficient conditions that the equation AXB+CYD=E is solvable.
作者
董晓
舒乾宇
DONG Xiao;SHU Qianyu(School of Mathematics Sciences,Sichuan Normal University,Chengdu 610066,Sichuan)
出处
《四川师范大学学报(自然科学版)》
2026年第1期123-134,共12页
Journal of Sichuan Normal University(Natural Science)
基金
国家自然科学基金(12071325)。
关键词
广义逆矩阵
乘法正则补元
矩阵方程
可解性
generalized inverse matrix
multiplicative regular complement
matrix equation
solvability
