On the bounds of maximal entries in the principal eigenvector of symmetric nonnegative matrix

Abstract

The upper bound of maximal entries in the principal eigenvector of a simple undirected connected graph is investigated in [Linear Algebra Appl. 310 (2000) 129]. We further investigate the maximal entry ymaxp in the principle eigenvector of symmetric nonnegative matrix with zero trace and obtain both sharp upper and lower bounds on the ymaxp. Particularly, this result answers the open question given in the above-mentioned reference