摘要
对一类矩阵(友阵)特征值的扰动进行讨论,首先给出这类矩阵谱范数和两个矩阵特征多项式之差的估计,然后得出:V(A,B)<(2n-1)·(2m_a)~1-1/n(sum from i=0 to (n-1) |b_i-a_i|)1/n;S_A(B)≤(2m_a)1-1/n(sum from i=0 to (n-1) |b_i-a_i|)1/n;S_A(B)≤n^(1/2n)m_2^(1-1/n)‖B-A‖_2^(1/n)。对于这类矩阵而言,此结果比 Ostrowski,Bhatia 和 Friedland 的结果更精确。
The perturbation of one kinds of matrices(companion matrix)is discussed in this paper.First,the authors estimated spectral norm of the matrix and difference of eigenpolynomial of two matrices and then obtained:V(A,B)<(2n-1)·(2m_α)^(1-1/n) (sum from i=0 to n-1|b_i-a_i|)^(1/n);S_A(B)≤(2m_α)^(1-1/n)(sum from i=0 to n-1|b_i-a_i|)^(1/n);S_A(B)≤n^(1/2n)m_2^(1-1/n)‖B- A‖_2^(1/n) For this kinds of matrices,this results are accurate than that of Ostrowski's and Friedland's.
出处
《东北林业大学学报》
CAS
CSCD
北大核心
1996年第2期59-61,共3页
Journal of Northeast Forestry University
关键词
矩阵
特征值
谱范数
Matrices
Eigenvalue
Spectral norm
