摘要
利用矩阵的欧氏范数得到矩阵特征值分布的两个上、下界估计，一个是利用方阵Ａ的迹和‖Ａ＋Ａ′２‖２表示出特征值实部、虚部的上、下界，其范围小于λ－ｔｒＡｎ≤ｎ－１ｎ（‖Ａ‖２Ｆ－１ｎ｜ｔｒＡ｜２）的估计范围且形式比较简便．另一个是利用‖Ａ‖２和‖ＡＡ′‖２表示出的特征值模的范围，与一些著名的估计相比更精确．讨论了它们在稳定性判定中的应用．
In this paper,we have obtained two kinds of estimations of upper and lower bounds for the distribution of eigenvalues of a matrix with its Euclidean norm.One is formulated by the trace of matrix A and ‖A+′2‖ 2 ,its area is smaller than the area estimated by λ -tr An≤ n-1n(‖A‖F 2-1n| tr A| 2 ) and its form is simpler.The other is formulated by ‖A‖ 2 and ‖A′‖ 2 , its area is more precise than other famous estimations.In addition,we have also discussed its application in stability theory.
出处
《山东师范大学学报（自然科学版）》
CAS
1999年第1期15-19,共5页
Journal of Shandong Normal University(Natural Science)
