两个矩阵谱改变量的上界估计

ESTIMATION OF UPPER BOUNDS FOR THE SPECTRAL VARIATION OF TWO MATRICES

关于两个矩阵A、B的谱改变量SA(B),R.Bhatia,S.Friedland和L.Elsner[1～3]得到SA(B)≤n 1/n(2M)1-1/n‖B-A‖1/n,这里M=max{‖A‖,‖B‖}其中‖A‖为A的谱范数.本文用矩阵A、B的奇异值给出SA(B)的上界估计,这个结果改进了上面给出的关于SA(B)的上界.

For the spectral variation of two matrices A、B,R.Bhatia,S.Friedland and L.Elsner have been proved that SA(B)≤n1n(2M)1-1n‖B-A‖1n,where M=max{‖A‖,‖B‖} and ‖‖be spectral norm.In this paper,we get estimation of upper bounds for SA(B) in terms of the singular values of A and B,which improve the inequality just mentioned.