A sharp upper bound on the maximal entry in the principal eigenvector of symmetric nonnegative matrix

作者：Das Kinkar Ch^*

来源：Linear Algebra and Its Applications, 2009, 431(8): 1340-1350.

DOI：10.1016/j.laa.2009.05.005

• Graph theory
• Principal eigenvector
• Symmetric nonnegative matrix
• Signless Laplacian matrix
• Spectral radius

An upper bound on the maximal entry in the principal eigenvector of a symmetric nonnegative matrix with zero diagonal entries is investigated in [S. Zhao, Y. Hong, On the bounds of maximal entries in the principal eigenvector of symmetric nonnegative matrix, Linear Algebra Appl. 340 (2002) 245-252]. We obtain a sharp upper bound on the maximal entry y(maxp) in the principal eigenvector of symmetric nonnegative matrix in terms of order, the spectral radius, the largest and the smallest diagonal entries of that matrix. Our bound is applicable for any symmetric nonnegative matrix and the upper bound of Zhao and Hong (2002) for the maximal entry y(maxp) follows as a special case. Moreover, we find an upperbound on maximal entry in the principal eigenvector for the signless Laplacian matrix of a graph.

• 出版日期2009-9-1