矩阵的秩和非零特征值个数的关系研究

发布时间：2018-02-12 15:15

本文关键词： 矩阵的秩特征值约当矩阵指数　出处：《上海理工大学学报》2017年01期 　论文类型：期刊论文

【摘要】：矩阵的秩和非零特征值个数是矩阵的重要不变量,研究二者关系也成为线性代数一个基本的问题.已有的文献分别给出了n阶矩阵的秩和非零特征值个数相等或相差n-1的充要条件.而矩阵指数又是矩阵的重要不变量,对复矩阵而言它指矩阵零特征值约当块的最大阶数.在已有文献基础上,研究了复数域上矩阵的秩和非零特征值个数二者的差与矩阵指数的关系,得到了矩阵的秩和非零特征值个数的差用矩阵指数刻画的一个充分必要条件,推广了已有文献的结果.
[Abstract]:The rank and the number of nonzero eigenvalues of a matrix are important invariants of the matrix. It is also a basic problem of linear algebra to study the relationship between them. The sufficient and necessary conditions for the number of rank and nonzero eigenvalues of matrix of order n to be equal or the difference between n-1 and matrix exponent are given respectively in the literature, and the matrix exponent is an important invariant of matrix. For complex matrix, it refers to the maximum order of matrix zero eigenvalue when block. On the basis of existing literatures, the relationship between the difference between the rank and the number of nonzero eigenvalues of matrix and the matrix exponent over complex field is studied. A sufficient and necessary condition for the difference of the number of rank and nonzero eigenvalues of a matrix to be characterized by matrix exponents is obtained.
【作者单位】：上海理工大学理学院;
【基金】：上海理工大学教师教学发展研究项目(CFTD17016Z)
【分类号】：O151.21

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