摘要
基于矩阵的相关性质,证明了数域上任意非零方阵均可分解为一个幂零阵与一个可逆阵之和,推进了已知相关结论.作为所得结果的应用,给出线性空间上线性变换的加法分解.
Based on the related properties of square matrices,we prove that every nonzero square matrix over a number filed can express as the sum of a nilpotent matrix and an inverible matrix,which generalize some known results.As an application,the additive decompositions of linear transformations over a linear space are provided.
作者
崔建
CUI Jian(School of Mathematics and Statistics,Anhui Normal University,Wuhu Anhui 241002,China)
出处
《大学数学》
2024年第2期100-105,共6页
College Mathematics
基金
安徽省高等学校省级质量工程项目(2021jyxm0517,2021xxkc058)。
关键词
非零方阵
可逆阵
幂零阵
fine分解
nonzero square matrix
invertible matrix
nilpotent matrix
fine decomposition
作者简介
崔建(1984-),男,博士,教授,从事代数学教学与研究.E-mail:cui368@ahnu.edu.cn。
