摘要
利用熟悉的矩阵的秩研究了含两个未知矩阵和的矩阵方程的解的存在性,得到了通解结构,即:(X,Y)=ε +K1ε1+K2ε2+…+Krεr,其中ε1,ε2,…,εr为解空间S={(X,Y)｜AXB+CYD=0}的一个基,ε 为矩阵方程AXB+CYD=E的一个特解,K1,K2,…,Kr为任意常数,进一步讨论了矩阵方程AXB+CYD=E的解法.
*'By using the rank of matrix, the matrix equation with two unknown matrix X,Y is considered, the existence of solution is studied, and the structure of the general solution for this equation is obtained, which is as following: (X,Y)=ε+k1ε1+k2ε2+...+krε1rwhere ε1,ε2,...,εr are a basis for the solution spaceS={(X,Y)|AXB+CYD=0},ε is a particular solution of the matrix equation AXB+CYD=E, k1,k2,...,kr are arbitrary constants. Further, the method of solving the matrix equation AXB+CYD=E is discussed.
出处
《吉林化工学院学报》
CAS
2003年第1期82-86,共5页
Journal of Jilin Institute of Chemical Technology
关键词
矩阵方程
秩
充要条件
唯一解
通解
matrix equation
rank
necessary and sufficient conditions
unique solution
general solution
