关于极大线性无关组和线性空间中基的扩充问题的讨论  

Discussion on the Expansion of Maximum Linear Independent Groups and Bases in Vector Space

作　　者：杨晓梅[1] 孟吉翔[1] 赵飚[1] 

机构地区：[1]新疆大学数学与系统科学学院,新疆 乌鲁木齐

出　　处：《理论数学》2023年第4期1079-1082,共4页Pure Mathematics

摘　　要：线性空间是线性代数中一个重要的研究对象,基与维数又能决定一个线性空间的结构,因此在已知的线性空间中找到满足要求的基是一个值得探讨的问题。本文根据线性空间中的扩充基定理,讨论了由给定线性无关的向量组扩充成一个极大线性无关组,以及在线性空间扩充成一组基的一般解法,旨在加深学生对极大线性无关组以及线性空间中基的理解。Linear space is an important research object in linear algebra, and the basis and dimension can determine the structure of a linear space. So it is a worthwhile problem to find the required basis in a linear space. In this paper, according to the expansion basis theorem in the linear space, we discuss how to find the maximum linear independent vector group or the basis for a given linear independent list in the linear space. It can promote the students’ understanding of the maximum linear independent vector group and the bases in the linear space.

关 键 词：线性空间 线性无关 极大线性无关组 基 

分 类 号：G63[文化科学—教育学]