矩阵可逆判定的等价命题  

Equivalent Propositions for Decision on the Invertibility of Matrix

作　　者：李斐[1] 张圣梅[1] 郭卉[2] LI Fei;ZHANG Sheng-mei;GUO Hui(School of Statistics and Applied Mathematics,Anhui University of Finance and Economics,Bengbu 233030,Anhui,China;Accounting College,Anhui University of Finance and Economics,Bengbu 233030,Anhui,China)

机构地区：[1]安徽财经大学统计与应用数学学院,安徽蚌埠233030 [2]安徽财经大学会计学院,安徽蚌埠233030

出　　处：《韶关学院学报》2020年第3期1-4,共4页Journal of Shaoguan University

基　　金：安徽省质量工程项目(2016tszy001);安徽财经大学校级教研项目(acjpkc201807).

摘　　要：总结高等代数课程中40个关于矩阵可逆的等价命题,把散落在课程各章节等价命题聚合在一起,旨在揭示高等代数课程中矩阵及其他重要概念之间的相互的联系,同时展现各章节概念与理论紧密相连,共同构成浑然一体的理论框架体系.This paper summarizes 40 equivalent propositions about matrix reversibility in the course of higher algebra,aggregating the equivalent propositions scattered in each chapter of the course,in order to reveal the interrelation between matrix and other important concepts in this course,and to show that the concepts in each chapter are closely connected with the theory,forming an integrated theoretical framework system.

关 键 词：可逆矩阵 向量 线性方程组 初等矩阵 线性空间与线性变换 正定矩阵 

分 类 号：O151[理学—数学] G642[理学—基础数学]