n个n维向量的等价性质及应用

The Equivalent Properties and Applications of N n-dimensional Vectors

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.