非负矩阵Perron根的上界

文章针对特殊的非负矩阵，应月简单的相似变换，使矩阵保持非负性且最大行和减小，从而得到行和为正非负矩阵Perron根的新上界．     

围长为g且有k个悬挂点的单圈图的谱半径和Laplacian谱半径

图的谱半径和Laplacian谱半径分别是图的邻接矩阵和Laplacian矩阵的最大特征值.本文中,我们分别刻画了围长为g且有k个悬挂点的单圈图的谱半径和Laplacian谱半径达到最大时的极图.     

The largest two Laplacian eigenvalues of a graph

In this article, we present lower bounds for the largest eigenvalue, the second largest eigenvalue and the sum of the two largest eigenvalues of the Laplacian matrix of a graph.     

The largest two Laplacian eigenvalues of a graph

In this article, we present lower bounds for the largest eigenvalue, the second largest eigenvalue and the sum of the two largest eigenvalues of the Laplacian matrix of a graph.     

Global exponential synchronization criterion for switched linear coupled dynamic networks

We in this paper develop a global exponential synchronization stability criterion for switched linear coupled network. By introducing a switching symmetric matrix, we prove that the stability of global exponential synchronization is governed by the largest eigenvalue of this switching symmetric matrix and the largest switching coupling strength. Meanwhile, we give the threshold of switching coupling strength which can make the switched linear network reach global exponential synchronization. Because the proposed criterion is on the basis of the original synchronization definition and the largest eigenvalue of the switching symmetric matrix, therefore, it is convenient to use in verifying global exponential synchronization of dynamic network with switching linear couplings.     

Non-white Wishart ensembles

We consider non-white Wishart ensembles , where X is a p×N random matrix with i.i.d. complex standard Gaussian entries and Σ is a covariance matrix, with fixed eigenvalues, close to the identity matrix. We prove that the largest eigenvalue of such random matrix ensembles exhibits a universal behavior in the large-N limit, provided Σ is “close enough” to the identity matrix. If not, we identify the limiting distribution of the largest eigenvalues, focusing on the case where the largest eigenvalues almost surely exit the support of the limiting Marchenko-Pastur's distribution.     

A note on the second largest eigenvalue of the laplacian matrix of a graph ∗

In this note, a lower bound for the second largest eigenvalue of the Laplacian matrix of a graph is given in terms of the second largest degree of the graph.     

A note on the second largest eigenvalue of the laplacian matrix of a graph

In this note, a lower bound for the second largest eigenvalue of the Laplacian matrix of a graph is given in terms of the second largest degree of the graph.     

Variational analysis of convexly generated spectral max functions

Mathematical Programming - The spectral abscissa is the largest real part of an eigenvalue of a matrix and the spectral radius is the largest modulus. Both are examples of spectral max...     

图的无号Laplace矩阵的最大特征值

The signless Laplacian matrix of a graph is the sum of its diagonal matrix of vertex degrees and its adjacency matrix. Li and Feng gave some basic results on the largest eigenvalue and characteristic polynomial of adjacency matrix of a graph in 1979. In this paper, we translate these results into the signless Laplacian matrix of a graph and obtain the similar results.     

An extremal sparsity property of the Jordan canonical form

We prove that among all the matrices that are similar to a given square complex matrix, the Jordan canonical form has the largest number of off-diagonal zero entries. We also characterize those matrices that attain this largest number.     

On the second largest Laplacian eigenvalues of graphs

The second largest Laplacian eigenvalue of a graph is the second largest eigenvalue of the associated Laplacian matrix. In this paper, we study extremal graphs for the extremal values of the second largest Laplacian eigenvalue and the Laplacian separator of a connected graph, respectively. All simple connected graphs with second largest Laplacian eigenvalue at most 3 are characterized. It is also shown that graphs with second largest Laplacian eigenvalue at most 3 are determined by their Laplacian spectrum. Moreover, the graphs with maximum and the second maximum Laplacian separators among all connected graphs are determined.     

双圈图的无符号拉普拉斯谱半径和谱展

The signless Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the smallest eigenvalue of its signless Laplacian matrix. In this paper, we determine the first to llth largest signless Laplacian spectral radii in the class of bicyclic graphs with n vertices. Moreover, the unique bicyclic graph with the largest or the second largest signless Laplacian spread among the class of connected bicyclic graphs of order n is determined, respectively.     

非负矩阵Perron根的上下界

1.引言 本文主要讨论非负矩阵,我们将用B≥0和B>0分别表示矩阵B是非负的和正的,也就是B的每一个元素是非负的和B的每一个元素是正的.用p(B)表示方阵B的谱半径,当B≥0时,p(B)也就是B的perron根. 设(n)={1,2,…,n},A=(ai,j)是n×n非负矩阵,我们称     

(分块)非负矩阵谱半径的界

<正>1引言若A=(a_(ij)),其中a_(ij)≥0,我们则称A为非负矩阵.ρ(A)表示A的谱半径,当A≥0时,ρ(A)就是A的Perron根.众所周知,若A≥0,则r_(min)(A)≤ρ(A)≤r_(max)(A),     

Some iterative methods for the largest positive definite solution to a class of nonlinear matrix equation

In this paper, we propose some inversion-free iteration methods for finding the largest positive definite solution of a class of nonlinear matrix equation. Then, we consider the properties of the solution for this nonlinear matrix equation. Also, we establish Newton’s iteration method for finding the largest positive definite solution and prove its quadratic convergence. Furthermore, we derive the semi-local convergence of the Newton’s iteration method. Finally, some numerical examples are presented to illustrate the effectiveness of the theoretical results and the behavior of the considered methods.     

亚高斯矩阵的精细非渐近尾界

在本文中,我们得到了亚高斯矩阵最大奇异值(软边)的精细非渐近尾界.以所得定理为基础, 我们研究了高斯Toeplitz矩阵的尾界.     

Residual Selection in A Projection Method for Convex Minimization Problems

We study a certain class of min-max optimization problems and we show that the solutions of such problems are, in some sense, degenerate, Two examples are given:minimization of the spectral radius of a symmetric matrix, minimization of the largest eigenvalue of a symmetric matrix     

Disjoint permutation matrices in complements of trees

The largest number of disjoint permutation matrices in the complement of a tree matrix is investigated     

Eigenvalue immobility measures for Markov chains 1

Two eigenvalue measures of immobility are proposed for social processes described by a Markov chain. One is the second largest eigenvalue modulus of the chain's transition matrix. The other is the second largest eigenvalue modulus of a closely related transition matrix. The two eigenvalue measures are compared to each other and to correlation and regression‐to‐the‐mean measures. In illustrative applications to intergenerational occupational mobility, the eigenvectors corresponding to the eigenvalue measures are found to be good proxies for occupational status rankings for a number of countries, thus reinforcing a pattern noted by Klatsky and Hodge and by Duncan‐Jones.