Some new bounds on the spectral radius of nonnegative matrices

Abstract

In this paper, we determine some new bounds for the spectral radius of a nonnegative matrix with respect to a new defined quantity, which can be considered as an average of average 2-row sums. The new formulas extend previous results using the row sums and the average 2-row sums of a nonnegative matrix. We also characterize the equality cases of the bounds if the matrix is irreducible and we provide illustrative examples comparing with the existing bounds.

Keywords

• nonnegative matrix
• spectral radius
• row sum
• 2-row sum
• average 2-row sum
• signless laplacian matrix