摘要
依据矩阵初等变换的定理及其性质,证明了任意1个n级复矩阵A,都存在1个n级可逆矩阵p,使得p-1AP=Λ为1个上三角矩阵.从而把求任意1个n级矩阵的特征值的问题通过初等变换转化为求上三角形矩阵的特征值的问题,并给出了求解的具体步骤.
Resting on some characters and theorems of the elementary transformation of matrix,this article proved that any n-order complex matrix A includes a n-order inverse matrix P,and makes p^(-1)AP=Λ a upper triangular matrix.Thus the solution to characteristic value of any n-order matrix is transferred to the solution to characteristic value of upper triangular matrix by the elementary transformation of the matrix,and the concrete step of the solution is given in this article.
出处
《河北北方学院学报（自然科学版）》
2006年第6期9-12,共4页
Journal of Hebei North University:Natural Science Edition
关键词
初等变换
上三角矩阵
特征值
elementary transformation
upper triangular matrix
characteristic value
