Upper bounds for the second largest eigenvalue of symmetric nonnegative matrices

被引：0
|
作者：
Kolotilina L.Y. [1 ]
机构：
[1] St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg
来源：
Journal of Mathematical Sciences | 2013年 / 191卷 / 1期
关键词：
Undirected Graph; Large Eigenvalue; Diagonal Entry; Adjacency Matrice; Nonnegative Matrice;
D O I：
10.1007/s10958-013-1305-x
中图分类号：
学科分类号：
摘要：
The paper suggests uppe bound on the second largest eigenvalue and the sum of two largest eigenvalues of symmetric nonnegative matrices and graphs. Conditions necessary and sufficient for some of the counds to be attained are established. Special attention is paid to the subclass of matrices with zero diagonal entries and with off-diagonal entries not exceeding unity, which obviously contains the adjacency matrices of undirected graphs. Bibliography: 8 titles. © 2013 Springer Science+Business Media New York.
引用
收藏
页码：75 / 88
页数：13
相关论文
共 50 条
  • [1] Bounds for the largest eigenvalue of nonnegative tensors
    He, Jun
    [J]. JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2016, 20 (07) : 1290 - 1301
  • [2] On the largest eigenvalue of a symmetric nonnegative tensor
    Zhou, Guanglu
    Qi, Liqun
    Wu, Soon-Yi
    [J]. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2013, 20 (06) : 913 - 928
  • [3] Sharp upper and lower bounds for largest eigenvalue of the Laplacian matrices of trees
    Hong, Y
    Zhang, XD
    [J]. DISCRETE MATHEMATICS, 2005, 296 (2-3) : 187 - 197
  • [4] On the inverse eigenvalue problem of symmetric nonnegative matrices
    Nazari, A. M.
    Mashayekhi, A.
    Nezami, A.
    [J]. MATHEMATICAL SCIENCES, 2020, 14 (01) : 11 - 19
  • [5] On the inverse eigenvalue problem of symmetric nonnegative matrices
    A. M. Nazari
    A. Mashayekhi
    A. Nezami
    [J]. Mathematical Sciences, 2020, 14 : 11 - 19
  • [6] On lower bounds for the largest eigenvalue of a symmetric matrix
    Walker, S. G.
    Van Mieghem, P.
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 429 (2-3) : 519 - 526
  • [7] UPPER BOUNDS FOR THE LARGEST EIGENVALUE OF A BIPARTITE GRAPH
    Merikoski, Jorma K.
    Kumar, Ravinder
    Rajput, Ram Asrey
    [J]. ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2013, 26 : 168 - 176
  • [8] UPPER EIGENVALUE BOUNDS FOR PENCILS OF MATRICES
    BEAUWENS, R
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1984, 62 (NOV) : 87 - 104
  • [9] Bounds for the second largest eigenvalue of a transition matrix
    Walker, Stephen G.
    [J]. LINEAR & MULTILINEAR ALGEBRA, 2011, 59 (07): : 755 - 760
  • [10] On Hankel matrices and the symmetric nonnegative inverse eigenvalue problem
    Julio, Ana, I
    Diaz, Roberto C.
    Herrera, Timoteo
    [J]. LINEAR & MULTILINEAR ALGEBRA, 2024, 72 (03): : 474 - 487
12345