摘要
该文研究了适合一定条件的方阵A∈C^(n×n)的对角化问题,应用矩阵的零化多项式、特征值、特征向量、矩阵的秩及其不等式等概念和理论,谨慎使用同一矩阵A的多项式,适合交换律的特殊性和非零幂零矩阵不可对角化的性质,给出了当矩阵A零化多项式的次数分别为2和3时,方阵A是否可以对角化的判别方法。这些方法对于矩阵论的教学与研究是十分有益的。
The diagonalization of a matrix A∈C^(n×n) is found and proved.Two results on diagonalization of matrices which annihilator polynomials with degree of 2,3 are obtained by the theories of annihilator polynomial,eigenvalue and eigenvector,the rank and their inequality,the same matrix A is suitable for the particularity of the commutative law and the property that non-zero nilpotent matrices cannot be diagonalized.These are beneficial for the teaching and research of matrix theory.
作者
刘慧娟
LIU Huijuan(Center of General Education,Zhengzhou Business College,Gongyi,Henan Province,451200 China)
出处
《科技资讯》
2021年第7期109-111,共3页
Science & Technology Information
基金
国家自然科学基金《高维流形中的拓扑递归结构研究》(项目编号:11801529)。
关键词
矩阵
特征值
特征向量
矩阵的秩
零化多项式
对角化
Matrix
Eigenvalue
Eigenvector
Rank of a matrix
Annihilator polynomial
Diagonalization
