| 关于矩阵方程求解的另一点注记 |
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| 引用本文： | 陈素琴,王琤.关于矩阵方程求解的另一点注记[J].大学数学,2021,37(1):63-67. |
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| 作者姓名： | 陈素琴 王琤 |
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| 作者单位： | 同济大学 数学科学学院,上海 200092;同济大学 数学科学学院,上海 200092 |
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| 基金项目： | 同济大学 2019 教学改革项目 |
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| 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.
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| 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 |
An Another Note on Solving a Matrix Equation |
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| CHEN Su-qin,WANG Cheng.An Another Note on Solving a Matrix Equation[J].College Mathematics,2021,37(1):63-67. |
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| Authors: | CHEN Su-qin WANG Cheng |
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| Institution: | (School of Mathematical Sciences, Tongji University, Shanghai 200092, China) |
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| Abstract: | 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. |
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| Keywords: | matrix equation full of column rank full of row rank equivalent matrices elementary operations of matrix equivalent vector set |
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