关于矩阵方程求解的另一点注记  

An Another Note on Solving a Matrix Equation

作　　者：陈素琴[1] 王琤[1] CHEN Su-qin;WANG Cheng(School of Mathematical Sciences, Tongji University, Shanghai 200092, China)

机构地区：[1]同济大学数学科学学院,上海200092

出　　处：《大学数学》2021年第1期63-67,共5页College Mathematics

基　　金：同济大学2019教学改革项目(1390104126)。

摘　　要：对任意给定的矩阵A∈Pm×n,B∈Pm×s(s≤n),探讨了矩阵方程AX=B有列满秩解,同时BY=A有行满秩解的充分必要条件,并且给出了基于矩阵的等价、齐次方程组的同解、向量组的等价及线性空间语言的推广.For any matrices A∈Pm×n,B∈Pm×s(s≤n),a necessary and sufficient condition for that the matrix equation AX=B has a full of column rank solution and that BY=A has a full of row rank one is discussed.Further more,it gives 4 equivalent expressions based on equivalent matrices,the same solutions for homogenous linear equations,equivalent vector set and the same linear spaces.

关 键 词：矩阵方程 列满秩 行满秩 矩阵的等价 矩阵的初等变换 向量组的等价 

分 类 号：O151.2[理学—基础数学]