• 论文 •

### 关于正规矩阵特征值的扰动

1. 中国科学院计算中心
• 出版日期:1984-03-14 发布日期:1984-03-14

### ON THE PERTURBATION OF THE EIGENVALUES OF A NORMAL MATRIX

1. Sun Ji-guang Computing Center, Academia Sinica
• Online:1984-03-14 Published:1984-03-14

Let N be a n×n normal matrix with eigenvalues v_1, v_2, …, v_n, and let A be an×n diagonalizable matrix, i. e., there is a nonsingular matrix Q such that Q~(-1)AQ=diag (α_1, α_2, …, α_n). It is proved that there exists a suitable permutation π of the set{1,2, …, n} such that(sum from i=1 to n |v_i-α_(π(i))|~2)~(1/2)≤||Q||_2||Q~(-1)||_2||A-N||_F,where || ||_2 denotes the spectral norm, and || ||_F the Frobenius norm.
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 [1] A. J. Hoffman, H. W. Wielandt, The variation of the spectrum of a normal matrix, Duke Math. J., 20 (1953) , 37-39． [2] W. Kahan, Spectra of nearly hermitian matrices, Proc. Amer. Math. Soc., 48 (1975) , 11-17． [3] G. W. Stewart, A note on non-Hermitian perturlations of Hermitian matrices, CNA-41, AD-745006, 1972．
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