n个n维向量的等价性质及应用  

The Equivalent Properties and Applications of N n-dimensional Vectors

作　　者：闻道君[1] 陈义安[1] WEN Dao-jun;CHEN Yi-an(School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, Chin)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067

出　　处：《重庆工商大学学报（自然科学版）》2018年第4期26-29,共4页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：重庆市前沿与应用基础研究(cstc2016jcyjA0101);高等学校大学数学教学与发展中心教学改革项目(CMC2016512);重庆工商大学首批课程改革建设项目(1792058)

摘　　要：基于"线性代数"课程的特点和在线优质资源辅助教学的推广,利用矩阵方法讨论了向量组的线性关系与行列式的值、矩阵的秩、初等变换、线性方程组的解和矩阵的特征值等问题之间的内在联系,建立了关于n个n维向量的一系列等价性质;最后,举例说明了系统掌握这些等价结论在解决一些综合性的考研试题方面的应用。Based on the characteristic of Linear Algebra course and popularity of assisted teaching with online high quality resources,the linear relations of N n-dimensional vectors are studied with the connection between determinant,rank of matrix,elementary transformation,solution of linear equations,eigenvalue of matrix and vector groups. A series of equivalent properties are obtained for N n-dimensional vectors. Moreover,some examples are given to illustrate the application of our results in solving some comprehensive questions of graduate record examination.

关 键 词：向量组 矩阵 线性相关 行列式 线性方程组 特征值 

分 类 号：O172.1[理学—数学] G420[理学—基础数学]