初等因子个数定理及应用  

The Number Theorem of Elementary Divisor and Its Application

作　　者：刘许成[1] 

机构地区：[1]潍坊学院数学系,山东潍坊261043

出　　处：《湖南理工学院学报（自然科学版）》2003年第2期12-15,共4页Journal of Hunan Institute of Science and Technology(Natural Sciences)

摘　　要：n级方阵A的特征根λ_i,重数为n_i,它所对应的初等因子的个数m_i=n_i+秩(A-λ_iE)-n,利用它得到了矩阵A与对角矩阵相似的充要条件和微分方程的求解定理。Let the eigenvalue of n-order square matrix be A; and its number of repetition be ni and the corresponding number of elementary divisor be mi = ni + rank( A-λiE)-n .Using it, we obtained the similar sufficient and necessary condition of A and diagonal matrix and the solving theorem of the system of differential equation.

关 键 词：初等因子 特征多项式 Wronski行列式 

分 类 号：O241.6[理学—计算数学]