浅谈向量组秩的稳定性  

On the Stability of Rank of Vector Group

作　　者：李东伟 宁荣健[1] Li Dongwei;NING Rongjian(School of Mathematics,Hefei University of Technology,Hefei 230601,China)

机构地区：[1]合肥工业大学数学学院,合肥230601

出　　处：《大学数学》2024年第6期76-80,共5页College Mathematics

基　　金：合肥工业大学青年教师教学研究项目(JYQN2223);安徽省自然科学基金(JZ2019AKZR0223)。

摘　　要：向量组的秩是向量组的重要特征.对于秩为n的n维向量组,本文研究当删除部分向量后对向量组秩的影响,并给出删除部分向量后不改变向量组秩的充要条件.特别地,对于含有m个向量的n维向量组(m>n),给出其任意n个向量都构成极大线性无关组的等价刻画.The rank is an important feature of vector group.For a set of n dimensional vectors with rank n,this paper investigates the impact on the rank of the vector group when some vectors are removed and provides necessary,and sufficient conditions for the rank of the vector group to remain unchanged after deleting some vectors.In particular,for a set of n dimensional vectors containing m vectors(m>n),an equivalent characterization is given for any n vectors to form a maximal linearly independent group.

关 键 词：向量组 秩 极大线性无关组 

分 类 号：O151.21[理学—数学]