共查询到20条相似文献,搜索用时 93 毫秒
1.
吕炯兴 《高等学校计算数学学报》1998,20(3):239-244
设A∈C~(n×n),B∈C~(k×k)均为Hermite矩阵,它们的特征值分别为{λ_j}_(j=1)~n和{μ_j}_(j=1)~k(k≤n);Q∈~(n×k)为列满秩矩阵.令 (1) 则存在A的k个特征值λ_(j_2),λ_(j_2),…,λ_(j_k),使得 (2) 其中σ_k为Q的最小奇异值,||·||_2表示矩阵的谱范数.这是著名的Kahan定理·1996年曹志浩等在[2]中将(2)加强为 (3) 这是Kahan的猜想.在本文中,我们讨论将Kahan定理中“B为k阶Hermite矩阵”改为B为k阶(任意)方阵后,特征值的扰动估计,有以下结果. 定理 设A∈C~(n×n)为Hermite矩阵,其特征值为{λ_j}_(j=1)~n,B∈C~(k×k)的特征值为{μ_j}_(j=1)~k,而Q∈C~(n×k)为列满秩矩阵.则存在A的k个特征值λ_(j_1),λ_(j_2),…,λ_(j_k),使得 相似文献
3.
4.
6.
刘彬清 《应用数学与计算数学学报》1999,13(2):73-77
本文对Ostrowski给出的关于矩阵的特征值估计作一些讨论,特征值分布特性被揭示,进而得到了一个判定矩阵非奇异性的充分条件. 相似文献
7.
8.
9.
In this paper we prove that for fixed positive integers α, β, m and m ≥ 2 the equation (?) holds for n = 2 only when m = 2, α = 3 and β = 1, which is another improvement of LeVeque's result, different from Yu's. 相似文献
10.
I.J.Matrix定理的更广泛推广 总被引:1,自引:1,他引:0
I.J.Matrix定理的更广泛推广张之正(河南洛阳师专数学系471022)近年来,数学通报连续讨论了1.J.Matrix定理的一些推广及其应用(文[l],[2]用复交函数中的留数定理,文[3J用初等方法,文[4]用线性代数中的Vandermonde... 相似文献
11.
12.
《Mathematical Methods in the Applied Sciences》2018,41(10):3632-3642
In this note, we obtain uniqueness results for Beltrami flow in both bounded and unbounded domain with nonempty boundary by establishing an elementary but useful formula involving operators div and curl. We also use this formula to deal with Maxwell and Stokes eigenvalue problems. 相似文献
13.
14.
We prove that for a compact Finsler manifold M with nonnegative weighted Ricci curvature,if its first closed(resp.Neumann)eigenvalue of Finsler-Laplacian attains the sharp lower bound,then M is isometric to a circle(resp.a segment).Moreover,a lower bound of the first eigenvalue of Finsler-Laplacian with Dirichlet boundary condition is also estimated.These generalize the corresponding results in recent literature. 相似文献
15.
16.
This paper discusses the first eigenvalue on a compact Riemann manifold with the negative lower bound Ricci curvature. Let M be a compact Riemann manifold with the Ricci curvature≥-R, R=const. ≥0 and d is the diameter of M. Our main result is that the first eigenvalue λ1 of M satisfies λ1≥π^2/d^2-0.518R. 相似文献
17.
本文对给定的可逆马氏链所对应的 Q-矩阵给出了它的第一非零特征值的 Monte Carlo估计方法 .具体做法是通过增加一个状态构造一个新的可逆马氏链 ,然后利用增加状态的击中时分布去估计第一非零特征值 . 相似文献
18.
PUI-FAI LEUNG 《Geometriae Dedicata》1997,66(2):159-162
We prove that if Mis a complete non-compact Riemannian manifold and 1(M)=0, then any C
2solution of uk> 0 is unbounded. We apply this result to obtain an estimate for the size of the image set of some types of maps between Riemannian manifolds. 相似文献
19.